Question

The zeros of the polynomial `x^2 - sqrt(2)x - 12` are ______.

Options

• `sqrt(2), -sqrt(2)`

• `3sqrt(2), -2sqrt(2)`

• `-3sqrt(2), 2sqrt(2)`

• `3sqrt(2), 2sqrt(2)`

Answer 1

The zeros of the polynomial `x^2 - sqrt(2)x - 12` are `underlinebb(3sqrt(2), -2sqrt(2))`.

Explanation:

`x^2 - sqrt(2)x - 12 = x^2 - 3sqrt(2)x + 2sqrt(2)x - 12`

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

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

∴  `x = 3sqrt(2)` or `x = -2sqrt(2)`