Question

It is given that the difference between the zeros of 4x² – 8kx + 9 is 4 and k > 0. Then, k = ?

Options

• `1/2`

• `3/2`

• `5/2`

• `7/2`

Answer 1

`bb(5/2)`

Explanation:

For 4x² – 8kx + 9 = 0, the sum of roots = 2k and the product = `9/4`. 

The difference of the roots is `|α - β| = sqrt((α + β)^2 - 4αβ)`

= `sqrt((2k)^2 - 4 xx (9/4))` 

= `sqrt(4k^2 - 9)`

Set this equal to 4: `sqrt(4k^2 - 9) = 4`

⇒ 4k² – 9 = 16

⇒ 4k² = 16 + 9

⇒ 4k² = 25

⇒ `k^2 = 25/4`

⇒ `k = ±5/2` 

Given k > 0, so k = `5/2`.