If \alpha, \beta are roots of x^2-3ax+a^2=0, find the value(s)

Slade Higgins

Slade Higgins

Answered question

2022-04-21

If α,β are roots of x23ax+a2=0, find the value(s) of a if α2+β2=74.

Answer & Explanation

Davon Friedman

Davon Friedman

Beginner2022-04-22Added 13 answers

We know that: α+β=3a and αβ=a2. Now, (α+β)22αβ=α2+β2
So, (α+β)22αβ=(3a)22a2=74
Now, just equate: 7a2=74a2=14, then a=±12.

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