Question

Zeroes of the polynomial p(x) = `x^2 - 3sqrt2  x + 4` are ______.

Options

• `2, sqrt2`

• `2sqrt2, sqrt2`

• `4sqrt2, -sqrt2`

• `sqrt2, 2`

Answer 1

Zeroes of the polynomial p(x) = `x^2 - 3sqrt2  x + 4` are `bbunderline(2sqrt2, sqrt2)`.

Explanation:

p (x) = `x^2 - 3sqrt(2x) + y`

using quadratic formula

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

a = 1

b = `−3sqrt2`

C = 4

`x = (3sqrt2 ± sqrt((-3sqrt2)^2 - 4 (1) (4)))/(2 (1))`

= `(3 sqrt2 ± sqrt(9xx2-16))/2`

= `(3sqrt2 ± sqrt(18-16))/2`

= `(3sqrt2 ± sqrt2)/2`

`x = (3sqrt2 + sqrt2)/2, x = (3sqrt2 - sqrt2)/2`

= `(4sqrt2)/2, (2sqrt2)/2`

x = `2sqrt2, sqrt2`