Class 10

Math

All topics

Quadratic Equations

Find a quadratic equation whose roots are $α,β$ such that $α+β=3$ and $α_{3}+β_{3}=9$.

Given $α+β=3−−−(1)$ & $α_{3}+β_{3}=9−−−−(2)$

From $(2)$ we get,

$(α+β)_{3}−3αβ(α+β)=9$

or, $27−9αβ=9$ [using $(1)$]

or, $9αβ=18$

or, $αβ=2−−−(3)$.

Now, the quadratic equation whose roots are $α$ & $β$ is

$x_{2}−(α+β)x+αβ=0$

or, $x_{2}−3x+2=0$. [ using $(1)$ & $(3)$].