Question

if two zero of the polynomial are 4x2 - 2x + (k-4) are reciprocal to each other find the value of k

Answer 1

let two zeroes be a and 1/a

product of zeroes = (k-4)/4

a × 1/a = ( k-4)/4

k - 4 = 4

k = 8

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Answer 2

Answer:

k = 8

Step-by-step explanation:

Let one zero be α.Then, the other zero is its reciprocal = 1/α.

Given Quadratic Equation is 4x² - 2x + (k - 4)

Here, a = 4, b = -2, c = (k - 4).

Product of roots:

We know that Product of roots = c/a.

⇒ α * 1/α = (k - 4)/4

⇒ 1 = (k - 4)/4

⇒ 4 = k - 4

⇒ k = 8.

Therefore, the value of k = 8.

Hope it helps!