Question

Find a quadratic polynomial whose sum and product of zeros are given as -3/2root5and -1/2

Answer 1

Given that,

$\alpha + \beta = \frac{- 3}{2\sqrt{5}}$

$\alpha \times \beta = \frac{-1}{2}$

To find,

A quadratic equation = ?

To form a quadratic polynomial when its zeros are given, there's a formula to frame the quadratic polynomial, which is stated below,

$\boxed{\bold{k[x^2 + (\alpha + \beta)x + (\alpha \times \beta)]}}$

Where k is a constant term.

Substituting the given values.

$\implies k[x^2 + (\frac{-3}{2\sqrt{5}})x + (\frac{-1}{2})]$

Substituting k = 2 (for cancelling 2 from denominator)

$\implies 2[x^2 + (\frac{-3}{2\sqrt{5}})x + (\frac{-1}{2})]$

$\implies 2x^2 + (\frac{-3}{\sqrt{5}}x) + (-1)$

Multiplying $\sqrt{5}$

$\implies 2\sqrt{5}x^2 + (-3)x + (-1)$

$\boxed{\bold{2\sqrt{5}x^2 -3x - 1}}$