5. If α and β are the zeros ofthe quadratic polynomial f(x)-kx44x+ 4

1.	5. If α and β are the zeros ofthe quadratic polynomial f(x)-kx44x+ 4 such that α=24then find the value of ksatisfying th
Answer» Given : f(x) = kx² + 4x + 4 and α and β are zero of f(x) so, α + β = -4/k and αβ = 4/k (α +β)² = α² + β² + 2αβ (-4/k)² = 24 + 2 × (4/k) 16/k² = 24 + 8/k 2/k² = 3 + 1/k 2/k² = (3k + 1)/k 2/k = ( 3k + 1) 2 = 3k² + k 3k² + k - 2 = 0 3k² + 3k - 2k - 2 = 0 3k ( k + 1) -2 ( k + 1) = 0 (3k - 2) ( k + 1) = 0 so, k = 2/9 and -1

5. If α and β are the zeros ofthe quadratic polynomial f(x)-kx44x+ 4 such that α=24then find the value of ksatisfying th

Answer»

Given : f(x) = kx² + 4x + 4 and α and β are zero of f(x)

so, α + β = -4/k and αβ = 4/k

(α +β)² = α² + β² + 2αβ

(-4/k)² = 24 + 2 × (4/k)

16/k² = 24 + 8/k

2/k² = 3 + 1/k

2/k² = (3k + 1)/k

2/k = ( 3k + 1)

2 = 3k² + k

3k² + k - 2 = 0

3k² + 3k - 2k - 2 = 0

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

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

so, k = 2/9 and -1