Question

If α and 1/α are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is ​

Answer 1

p(x) = 2x² – x + 8k

• It's zeroes are α & 1/α

From relationship of zeroes and coefficients of a quadratic polynomial, we have,

• αβ = (8k)/2

Here,

=> α × 1/α = 8k/2

=> 1 = 4k

=> k = ¼

Answer 2

Given: α and 1/α are the zeroes of the quadratic polynomial $2 {x}^{2} - x + 8k$

To find: The value of k

Solution: α and 1/α are the zeroes.

Product of the zeroes

= α × 1/α

= 1

In a quadratic polynomial $a {x}^{2} + bx + c$:

The sum of zeros = -b/a

The product of zeros = c/a

Here, in the given polynomial:

a = 2, b = -1 and c = 8k

Product of zeros according to the above mentioned formula

= c/a

= 8k/2

= 4k

Therefore,

4k = 1

=> k = 1/4

Therefore, the value of k is 1/4.