If the sum and the product of the zeroes of polynomial ax² - 5x + c are equal to 10 each. Find the values of a and c.

The sum and product of the polynomial have a direct relationship with the coefficients.

Answer: The value of a = 1/2 and value of c = 5 for ax² - 5x + c.

Let's find the value of a and c.

Explanation:

On comparing ax² - 5x + c with ax² + bx + c, we get b = -5.

Given,

In the quadratic polynomial ax² - 5x + c, the sum and product of zeroes is equal to 10 each.

⇒ - b / a = sum of the zeroes 

⇒ - (- 5) / a = 10

⇒ a = 5 / 10 = 1 / 2

Similarly, 

⇒ c / a = product of zeroes

⇒ c / a = 10

⇒ c = 5 ( by using a = 1/2)

Thus, the value of a = 1/2 and value of c = 5.