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

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.

Answer:

If the Sum and the Product of the Zeros of Polynomial ax² - 5x + c are Equal to 10 Each. The Values of a = 1/2 and c = 5

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