Question

If the sum and the product of zeroes of a quadratic polynomial are `2sqrt3` and 3 respectively, then a quadratic polynomial is ______.

Options

• `x^2 + 2sqrt3x - 3`

• `(x - sqrt3)^2`

• `x^2 - 2sqrt3x - 3`

• `x^2 + 2sqrt3x + 3`

Answer 1

If the sum and the product of zeroes of a quadratic polynomial are `2sqrt3` and 3 respectively, then a quadratic polynomial is `bbunderline((x - sqrt3)^2)`.

Explanation:

If α and β are the zeroes of a quadratic polynomial, then

Given, `alpha + beta = 2sqrt3 and alphabeta = 3`

Now, Quadratic polynomial is

p (x) = x² − (α + β) x + αβ

 `x^2 - (2sqrt3)x + (3)`

= `x^2 - 2sqrt3x + 3`

= `(x - sqrt3)^2`