## How do you find the quadratic equation if the roots are given?

The formula to find the roots of the quadratic equation is x = −b±√b2−4ac2a − b ± b 2 − 4 a c 2 a . The sum of the roots of a quadratic equation is α + β = -b/a = – Coefficient of x/ Coefficient of x2. The quadratic equation having roots α, β, is x2 – (α + β)x + αβ = 0.

### What is the quadratic equation of 3/4 and 2?

The standard quadratic equation using the given set of solutions {−34,2} { – 3 4 , 2 } is y=x2−5×4−32 y = x 2 – 5 x 4 – 3 2 .

What is the quadratic equation if the roots are 0 and 4 *?

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x2+4x=0.

What is the quadratic equation of 3 4?

The standard quadratic equation using the given set of solutions {3,−4} is y=x2+x−12 y = x 2 + x – 12 .

## What is the quadratic equation whose roots are 5 and 2?

The standard quadratic equation using the given set of solutions {5,2} is y=x2−7x+10 y = x 2 – 7 x + 10 .

### What is the quadratic equation if its roots are 5 and 8?

2(x−5)(x−8) . Using the distributive property, this is: 2×2−16x−10x+80=2×2−26x+80 . Like I said before, using any a∈R with a≠0 will be acceptable.

What is the equation if the roots are and 0?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal….Nature Of Roots.

b2 – 4ac > 0 Real and unequal
b2 – 4ac > 0 (is aperfect square and a or b is irrational) Irrational

How many roots does a quadratic equation have in standard form?

A quadratic equation in its standard form is represented as: ax2 +bx+c a x 2 + b x + c = 0 0, where a, b and c a, b a n d c are real numbers such that a≠ 0 a ≠ 0 and x x is a variable. The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots.

## How do you find the roots of an equation?

First, find the roots or solutions your way, and then use the roots calculator to confirm your answer. The calculator uses the quadratic formula to find the roots of a quadratic equation. Need to learn Algebra through examples?

### How do you find a quadratic function with no real roots?

An example of a quadratic function with no real roots is given by, f ( x) = x2 − 3 x + 4. b2 −4 ac = (−3) 2 − 4 · 1 · 4 = 9 − 16 = −7.

How to find the root of a quadratic equation with opposite sign?

The roots of quadratic equation are equal in magnitude but of opposite sign if b = 0 and ac < 0; The root with greater magnitude is negative if the sign of a = sign of b × sign of c; If a > 0, c < 0 or a > 0, c > 0; the roots of quadratic equation will have opposite sign; If y = ax 2 + bx + c is positive for all real values of x, a > 0 and D < 0

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