Question

If the zeroes of the given polynomial are reciprocal of each other, find the value of k.

4x^2 - 2x + k -2

Answer 1

Answer: 6

Explanation:

Given,

Polynomial = 4x² - 2x + (k - 2)

Let the zeroes of polynomial be x and 1/x

==> 4x² - 2x + (k - 2)

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

We know that,

Product of zeroes = c/a

==> x × 1/x = (k - 2)/4

==> 1 = (k - 2)/ 4

==> 1 × 4 = k - 2

==> 4 = k - 2

==> k = 6

Therefore, the value of k is 6.

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Value \: of \: k = 6 }}}}$

Given:-

• Polynomial = 4x² - 2x + k-2

• zeroes = reciprocal of each other.

To find:-

• Value of k = ?

Given polynomial = 4x² - 2x + (k - 2)

$\sf Let\: the \:zeroes\: be\: \: \alpha \: \& \: \dfrac{1}{\alpha}$

Comparing with the equation : ax² + bx + c,we get:-

⇒ a = 4

⇒ b = -2

⇒ c = (k - 2)

We know that,

➳ Product of zeroes = c/a

➳ $\sf \cancel{\alpha} \times \dfrac{1}{\cancel{\alpha}} = \dfrac{k - 2}{4}$

➳ 1 = (k - 2)/4

➳ 4 = k - 2

➳ k - 2 - 4 = 0

➳ k = 6

$\therefore{\underline{\boxed{\sf\green{Value \: of \: k = 6 }}}}$