If the Sum of the Squares of Zeros of Quadratic Polynomial F(X)= x^2 - 8 x + K is 40, Find k

If the Sum of the Squares of Zeros of Quadratic Polynomial F(X)= x^2 - 8 x + K is 40, Find k

Solution:

Let's find the sum of the squares of the zeros of the quadratic polynomial F(x) = x² - 8x + K.

The sum of the squares of the zeros can be found using the following relationship: Sum of squares of zeros = (α² + β²)

In the quadratic polynomial F(x) = x² - 8x + K, let α and β be the zeros. Therefore, we have: α + β = 8 (from the coefficient of the linear term) αβ = K (from the constant term)

We are given that the sum of the squares of the zeros is 40. So, we have: (α² + β²) = 40

To solve for K, we can express (α² + β²) in terms of α + β and αβ using the identity: (α² + β²) = (α + β)² - 2αβ

Substituting the values we know, we get: (α + β)² - 2αβ = 40 (8)² - 2K = 40 64 - 2K = 40 -2K = 40 - 64 -2K = -24 K = (-24)/(-2) K = 12

Therefore, the value of K is 12.

Answer:

When the Sum of the Squares of the Zeros of the Quadratic Polynomial F(x) = x² - 8x + K is 40, the Value of K is 12

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