Math, asked by pratapchittimalla, 1 year ago

if al and a2 are zeroes of polynomial kx^2 + 4x + 4 and if a1^2 + a2^2 = 24, find the value of k

Answers

Answered by Anonymous
3

Answer:

2/3 or - 1

Step-by-step explanation:

a1 and a2 are the zeroes of kx² + 4x + 4

Comparing the given polynimial with ax² + bx + c we get,

  • a = k
  • b = 4
  • c = 4

Sum of zeroes = a1 + a2 = - b / a = - 4 / k

Product of zeroes = a1.a2 = c / a = 4 / k

Given :

a1² + a2² = 24

Using algebraic identity ( a1 + a2 )² = a1² + a2² + 2a1.a2

⇒ ( - 4 / k )² = 24 + 2( 4 / k )

⇒ 16 / k² = 24 + 8 / k

Dividing by 8 on both sides

⇒ 2 / k² = 3 + 1 / k

⇒ 0 = 3 + 1 / k - 2 / k²

Multiplying by k² on sides

⇒ 0 = 3k² + k - 2

⇒ 3k² + k - 2 =0

⇒ 3k² + 3k - 2k - 2 = 0

⇒ 3k( k + 1 ) - 2( k + 1 ) = 0

⇒ ( 3k - 2 )( k + 1 ) = 0

⇒ 3k - 2 = 0 or k + 1 = 0

⇒ k = 2/3 or k = - 1

Therefore the value of k is 2/3 or - 1.

Similar questions