Question

# $α$ and $β$ are the zeros of a polynomial, such that $α+β=6$ and $αβ=4$. Identify the polynomial.

**A**

## $x_{2}−6x+4$

**B**

## $a_{2}+6a+4$

**C**

## $p_{2}+6p−4$

**D**

## $m_{2}−6m−4$

Easy

Solution

Verified by GMS

We can also write $p(x)$ in this form also

$p(x)=x_{2}−a−b x+ac $

$⇒p(x)=x_{2}−(α+β)x+αβ$

Now given that $α+β=6$ and $αβ=4$

Substituting these values we get

$p(x)=x_{2}−(6)x+4$ is the required polynomial.