Proving roots of quadratic equations If \(\displaystyle\alpha,\beta\) are

juctommaccedo662f

juctommaccedo662f

Answered question

2022-03-30

Proving roots of quadratic equations
If α,β are the roots of the quadratic equation ax2+bx+c=0, obtain the equation whose roots are 1α3 and 1β3.
If, in the above equation αβ2=1, prove that a3+c3+abc=0.

Answer & Explanation

Melody Gamble

Melody Gamble

Beginner2022-03-31Added 10 answers

So α=b±b24ac2a and let β=bb24ac2a
so αβ=b+b24ac2abb24ac2a=
b2b24ac24a2=4ac4a2=ca
And so if αβ2=1 then β=1αβ=ac
Plug x=β=ac into ax2+bx+c=0
and we get aβ2+bβ+c=
a3c2+abc+c=0
so a3+abc+c3=0

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