Class 10

Math

All topics

Quadratic Equations

Let $α+β=3$ and $α_{3}+β_{3}=7$, then find the equation of the quadratic equation whose roots are $α,β$.

$α+β=3$......(1)

And

$α_{3}+β_{3}=7$

or, $(α+β)_{3}−3α.β(α+β)=7$

or, $3_{3}−9α.β=7$ [ Using (1)]

or, $9α.β=2$

or, $α.β=920 $......(2).

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

$x_{2}−(α+β)x+α.β=0$

or, $x_{2}−3x+920 =0$

or, $9x_{2}−27x+20=0$. [Using (1) and (2)]