If the Sum of the Squares of Zeros of Quadratic Polynomial F(X)= x^2 – 8 x + K is 40, Find k
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If the sum of the squares of zeros of quadratic polynomial F(X)= x² – 8 x + K is 40, find k
For the given quadratic polynomial F(x) = x² – 8x + K, assume α and β be the zeros of F(x). As it is mentioned that the sum of the squares of the zeros is (α² + β²) hence (α² + β²) = 40.
To find the solution, use α + β = 8 and αβ = K. Further use the identity (α² + β²) = (α + β)² – 2αβ.
Substitute the values into the identity: (8)² – 2K = 40.
Simplify the equation and solve for K.
Table of content
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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