if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k​

2 thoughts on “if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k​”

1. Question

   • if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k

   Answer

   → α × β = c/a

   → α ×1/α = (k-4)/4

   → 1 × 4 = (k-4)

   → 4 = k-4

   → 4+4 = k

   → k = 8

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2. Step-by-step explanation:

   Given:–

   α and 1/α are the zeroes of the polynomial 4x^2+2x+(k-4)

   To find:–

   Find the value of k ?

   Solution:–

   Given that

   Given Quardratic polynomial p(x) = 4x^2+2x+(k-4)

   On Comparing this with the standard quadratic Polynomial ax^2+bx+c then

   a = 4

   b=2

   c=k-4

   Given zeroes are α and 1/α

   We Know that

   Sum of the zeroes = -b/a

   α +( 1/α) = -2/4

   α + (1/α) = -1/2————(1)

   Product of the zeroes = c/a

   =>( α )(1/α) = (k-4)/2

   => 1 = (k-4)/2

   => 2=k-4

   => k-4 = 2

   => k = 2+4

   => k =6

   Therefore,k = 6

   Answer:–

   The value of k for the given problem is 6

   Used formulae:–

   1.The standard quadratic Polynomial ax^2+bx+c

   2.Sum of the zeroes = -b/a

   3.Product of the zeroes = c/a

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