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.
On comparing ax2 - 5x + c with ax2 + bx + c, we get b = -5.
⇒ - b / a = sum of the zeroes
⇒ - (- 5) / a = 10
⇒ a = 5 / 10 = 1 / 2
⇒ 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.