Question

If a and b are the zeros of the polynomial 4x^2-2x+(k-4)and a=1/b,find the value of k(2)

Answer 1

Step-by-step explanation:

Given:

If a and b are the zeros of the polynomial 4x² - 2x + (k - 4) and a = 1/b.

To find:

The value of k.

Solution:

a and b are the zeros of the polynomial.

Given polynomial 4x² - 2x + (k - 4) and a = 1/b.

Compare the given polynomial

ax² + bx + c

Here,

• a = 4
• b = - 2
• c = k - 4

By rule of product of roots, we have:

Product of zeros = c/a

• b + 1/b = (k - 4)/4

• 1 = (k - 4)/4

• 1 × 4 = k - 4

• 4 = k - 4

• k = 4 + 4

• k = 8

∴ The value of k = 8

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