If α and β are the zeroes of a polynomial such that α+β=6 and αβ=4 then write the quadratic polynomial.

Question

If $α$ and $β$ are the zeroes of a polynomial such that $α + β = 6$ and $α β = 4$ then write the quadratic polynomial.

Easy

Solution

Verified by GMS

Given that,
$α + β = 6$ And $α β = 4$

The quadratic polynomial whose zeroes are $α, β$ is,

$f (x) = k [x^{2} - (α + β) x + α β]$

$= k [x^{2} - 6 x + 4]$

Where $^{'} k^{'}$ is any non zero real number

Getting Info...

Copy