First Root of Quadratic Equation given Discriminant Calculator

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Quadratic Equation

✖Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation.ⓘ Numerical Coefficient b of Quadratic Equation [b]			+10% -10%
✖Discriminant of Quadratic Equation is the expression that shows the nature of roots of the Quadratic Equation.ⓘ Discriminant of Quadratic Equation [D]			+10% -10%
✖Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation.ⓘ Numerical Coefficient a of Quadratic Equation [a]			+10% -10%

✖First Root of Quadratic Equation is the value of one of the variables satisfying the given quadratic equation f(x), such that f(x1) = 0.ⓘ First Root of Quadratic Equation given Discriminant [x₁]

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First Root of Quadratic Equation given Discriminant

Formula

`"x"_{"1"} = (-"b"+sqrt("D"))/(2*"a")`

Example

`"3"=(-"8"+sqrt("400"))/(2*"2")`

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First Root of Quadratic Equation given Discriminant Solution

STEP 0: Pre-Calculation Summary

Formula Used

First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)
x₁ = (-b+sqrt(D))/(2*a)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

First Root of Quadratic Equation - First Root of Quadratic Equation is the value of one of the variables satisfying the given quadratic equation f(x), such that f(x1) = 0.
Numerical Coefficient b of Quadratic Equation - Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation.
Discriminant of Quadratic Equation - Discriminant of Quadratic Equation is the expression that shows the nature of roots of the Quadratic Equation.
Numerical Coefficient a of Quadratic Equation - Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation.

STEP 1: Convert Input(s) to Base Unit

Numerical Coefficient b of Quadratic Equation: 8 --> No Conversion Required
Discriminant of Quadratic Equation: 400 --> No Conversion Required
Numerical Coefficient a of Quadratic Equation: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x₁ = (-b+sqrt(D))/(2*a) --> (-8+sqrt(400))/(2*2)

Evaluating ... ...

x₁ = 3

STEP 3: Convert Result to Output's Unit

3 --> No Conversion Required

FINAL ANSWER

3 <-- First Root of Quadratic Equation

(Calculation completed in 00.004 seconds)

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< 17 Quadratic Equation Calculators

Second Root of Quadratic Equation

Go Second Root of Quadratic Equation = (-(Numerical Coefficient b of Quadratic Equation)-sqrt(Numerical Coefficient b of Quadratic Equation^2-4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

First Root of Quadratic Equation

Go First Root of Quadratic Equation = (-(Numerical Coefficient b of Quadratic Equation)+sqrt(Numerical Coefficient b of Quadratic Equation^2-4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

Value of Quadratic Equation

Go Value of Quadratic Equation = (Numerical Coefficient a of Quadratic Equation*Value of X of Quadratic Equation^2)+(Numerical Coefficient b of Quadratic Equation*Value of X of Quadratic Equation)+(Numerical Coefficient c of Quadratic Equation)

Maximum or Minimum Value of Quadratic Equation

Go Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation)

Numerical Coefficient 'b' of Quadratic Equation

Go Numerical Coefficient b of Quadratic Equation = sqrt(Discriminant of Quadratic Equation+(4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))

Second Root of Quadratic Equation given Discriminant

Go Second Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation-sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

First Root of Quadratic Equation given Discriminant

Go First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

Numerical Coefficient 'a' of Quadratic Equation

Go Numerical Coefficient a of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2-Discriminant of Quadratic Equation)/(4*Numerical Coefficient c of Quadratic Equation)

Numerical Coefficient 'c' of Quadratic Equation

Go Numerical Coefficient c of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2-Discriminant of Quadratic Equation)/(4*Numerical Coefficient a of Quadratic Equation)

Discriminant of Quadratic Equation

Go Discriminant of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2)-(4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)

Difference of Roots of Quadratic Equation

Go Difference of Roots of Quadratic Equation = sqrt(Discriminant of Quadratic Equation)/Numerical Coefficient a of Quadratic Equation

Value of X for Maximum or Minimum Value of Quadratic Equation

Go Value of X for Maximum/Minimum Value of f(X) = -Numerical Coefficient b of Quadratic Equation/(2*Numerical Coefficient a of Quadratic Equation)

Maximum or Minimum Value of Quadratic Equation using Discriminant

Go Maximum/Minimum Value of Quadratic Equation = -Discriminant of Quadratic Equation/(4*Numerical Coefficient a of Quadratic Equation)

Product of Roots of Quadratic Equation

Go Product of Roots = Numerical Coefficient c of Quadratic Equation/Numerical Coefficient a of Quadratic Equation

Sum of Roots of Quadratic Equation

Go Sum of Roots = -Numerical Coefficient b of Quadratic Equation/Numerical Coefficient a of Quadratic Equation

Product of Roots of Quadratic Equation given Roots

Go Product of Roots = First Root of Quadratic Equation*Second Root of Quadratic Equation

Sum of Roots of Quadratic Equation given Roots

Go Sum of Roots = (First Root of Quadratic Equation)+(Second Root of Quadratic Equation)

First Root of Quadratic Equation given Discriminant Formula

What is a Quadratic Equation?

A Quadratic Equation is an algebraic equation in some variable x with the highest degree of terms being 2. The Quadratic Equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a Quadratic Equation is the coefficient of x2 is a non-zero term(a ≠ 0). If the discriminant is positive, then the Quadratic Equation will have two real roots. If the discriminant is zero, then the Quadratic Equation will have one real root. If the discriminant is negative, then the Quadratic Equation will not have any real roots.

What is a discriminant?

The discriminant of a quadratic equation is a function of its coefficients which gives an idea about the nature of its roots. For a quadratic polynomial a*x^2 + b*x + c, the formula of discriminant is given by the following equation: D= b^2-4*a*c

How to Calculate First Root of Quadratic Equation given Discriminant?

First Root of Quadratic Equation given Discriminant calculator uses First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation) to calculate the First Root of Quadratic Equation, The First Root of Quadratic Equation given Discriminant is defined as one of the solutions (or roots) obtained when solving the quadratic equation. First Root of Quadratic Equation is denoted by x₁ symbol.

How to calculate First Root of Quadratic Equation given Discriminant using this online calculator? To use this online calculator for First Root of Quadratic Equation given Discriminant, enter Numerical Coefficient b of Quadratic Equation (b), Discriminant of Quadratic Equation (D) & Numerical Coefficient a of Quadratic Equation (a) and hit the calculate button. Here is how the First Root of Quadratic Equation given Discriminant calculation can be explained with given input values -> 3 = (-8+sqrt(400))/(2*2).

FAQ

What is First Root of Quadratic Equation given Discriminant?

The First Root of Quadratic Equation given Discriminant is defined as one of the solutions (or roots) obtained when solving the quadratic equation and is represented as x₁ = (-b+sqrt(D))/(2*a) or First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation). Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation, Discriminant of Quadratic Equation is the expression that shows the nature of roots of the Quadratic Equation & Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation.

How to calculate First Root of Quadratic Equation given Discriminant?

The First Root of Quadratic Equation given Discriminant is defined as one of the solutions (or roots) obtained when solving the quadratic equation is calculated using First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation). To calculate First Root of Quadratic Equation given Discriminant, you need Numerical Coefficient b of Quadratic Equation (b), Discriminant of Quadratic Equation (D) & Numerical Coefficient a of Quadratic Equation (a). With our tool, you need to enter the respective value for Numerical Coefficient b of Quadratic Equation, Discriminant of Quadratic Equation & Numerical Coefficient a of Quadratic Equation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate First Root of Quadratic Equation?

In this formula, First Root of Quadratic Equation uses Numerical Coefficient b of Quadratic Equation, Discriminant of Quadratic Equation & Numerical Coefficient a of Quadratic Equation. We can use 1 other way(s) to calculate the same, which is/are as follows -

First Root of Quadratic Equation = (-(Numerical Coefficient b of Quadratic Equation)+sqrt(Numerical Coefficient b of Quadratic Equation^2-4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

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