\(\displaystyle\alpha,\beta\) are roots of the equation

Dexter Odom

Dexter Odom

Answered question

2022-03-31

α,β are roots of the equation 3x2(m2)x+(m5)=0 such that α5+β5=33. Find the value of m.

Answer & Explanation

Brennan Thompson

Brennan Thompson

Beginner2022-04-01Added 10 answers

We have, 3x2(m2)x+(m5)=0. Notice that sum of the coefficients is 0, so one root is 1 and another root is m53.
15+(m53)5=33
m53=2m=11
Jaslyn Allison

Jaslyn Allison

Beginner2022-04-02Added 13 answers

Observe,
α+β=m23   and   αβ=m53α+β=αβ+1(α1)(β1)=0
Therefore, either α=1 or β=1. Since α5+β5=33, the roots of the quadratic must be 1 and 2. Plugging this into one of the previous equations, we must have m=11.
Note: The quadratic equation is 3x29x+6=3(x1)(x2)=0

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