# If the Sum and the Product of the Zeros of Polynomial ax2 – 5x + c are Equal to 10 Each. Find the Values of a and c

By BYJU'S Exam Prep

Updated on: October 17th, 2023

If the sum and the product of the zeroes of polynomial ax– 5x + c are equal to 10 each. Find the values of a and c.

In the quadratic polynomial ax² – 5x + c, we are given that the sum and product of the zeros are equal to 10 each.

Using the formula for the sum of the zeros (-b/a) and the product of the zeros (c/a), we can find the values of a and c.

We can verify the result we can find the zeros of the quadratic polynomial ax² – 5x + c using the quadratic formula and check if their sum and product match the given conditions.

## If the Sum and the Product of the Zeros of Polynomial ax2 – 5x + c are Equal to 10 Each. Find the Values of a and c

Solution:

Given that the sum and the product of the zeros of the polynomial ax² – 5x + c are both equal to 10, we can find the values of a and c.

The sum of the zeros is α + β = 10.

The product of the zeros is αβ = 10

Sum of the zeros: -b/a = 10 Plugging in the values -5 for b, we will get:

– (- 5) / a = 10

⇒ a = 1/2,

Now, Product of the zeros: c/a = 10

Plugging in the values c and a = 1/2, we have:

c / (1/2) = 10

c * (2/1) = 10

2c = 10 c = 10 / 2

c = 5

Therefore, the values of a and c are a = 1/2 and c = 5, respectively.