Question

The zeros of the polynomial `4x^2 + 5sqrt(2)x - 3` are ______.

Options

• `-3sqrt(2), sqrt(2)`

• `-3sqrt(2), sqrt(2)/2`

• `(-3sqrt(2))/2, sqrt(2)/4`

• none of these

Answer 1

The zeros of the polynomial `4x^2 + 5sqrt(2)x - 3` are `underlinebb((-3sqrt(2))/2, sqrt(2)/4)`.

Explanation:

`4x^2 + 5sqrt(2)x - 3 = 4x^2 + 6sqrt(2)x - sqrt(2)x - 3`

= `2sqrt(2)x(sqrt(2)x + 3) - (sqrt(2)x + 3)`

= `(sqrt(2)x + 3)(2sqrt(2)x - 1)`

∴ `x = (-3)/sqrt(2)`

= `(-3)/sqrt(2) xx sqrt(2)/sqrt(2)`

= `(-3sqrt(2))/2`

or

`x = 1/(2sqrt(2))`

= `1/(2sqrt(2)) xx sqrt(2)/sqrt(2)`

= `sqrt(2)/4`