Question

if alpha and beta are the zeros of the polynomial kx2+3x+2 such that Alpha square plus beta square + alpha beta minus 1 upon 25 find the value of k ​

Answer 1

According to the question,

α and β are the zeroes of polynomial kx² + 4x + 4

a = k

-b = -4c = 4

α + β = -b/a = -4/k

αβ = c/a = 4/k

Given => α² + β² = 24

=> (α + β)² - 2αβ = 24

=> (-4/k)² - 2×4/k = 24

=> 16/k² - 8/k = 24

=> 16 - 8k = 24k²

=> 24k² + 8k - 16 = 0

=> 3k² + k - 2 = 0

=> 3k² + 3k - 2k - 2 = 0

=> 3k(k + 1) - 2(k + 1) = 0

=> (3k - 2)(k + 1) = 0

=> k = 2/3 or -1