# Find the Sum and Product of Roots of the Polynomial 2x²+x-5=0

By BYJU'S Exam Prep

Updated on: October 17th, 2023

Find the sum and product of roots of the polynomial 2x²+x-5=0.

We will start with the polynomial equation and identify the coefficients of the polynomial: a, b, and c. We can either use the quadratic formula to find the roots of the polynomial and then find the answer or we find the sum of the roots using the formula: α + β = -b/a. And substitute the value of b and a into the formula.
Simplify the expression to obtain the sum of the roots.
Then we can find the product of the roots (α × β) using the formula: α × β = c/a. By substituting the value of c and a into the formula.

## Find the Sum and Product of Roots of the Polynomial 2x²+x-5=0

Solution:

To find the sum and product of the roots of the polynomial 2x² + x – 5 = 0, we can use the relations between the coefficients and the roots of a quadratic equation.

The given quadratic equation is in the form of ax² + bx + c = 0, where a = 2, b = 1, and c = -5.

The sum of the roots (α + β) can be found using the formula: α + β = -b/a.

Substituting the values into the formula, we have: α + β = -(1)/(2) = -1/2.

The product of the roots (αβ) can be found using the formula: αβ = c/a.

Substituting the values into the formula, we have: αβ = (-5)/(2) = -5/2.

Therefore, the sum of the roots is -1/2 and the product of the roots is -5/2.