Let alpha and beta be the roots of the equation (k-1)x^2+(1-5k)x+4k=0 where k is real and k does not equal to 1. Find the value of k if alpha=beta ?

1 Answer
Jun 1, 2018

k=-1/3

Explanation:

Let α and β be the roots of the equation
(k−1)x²+(1−5k)x+4k=0, where k is real and k does not equal to 1. Find the value of k if α=β
Well, you don't have to worry actually: you just need to understand what you need to do.
What are α and β related to the equation ? They are the solutions, sure. So, if we have α=β, it means that Δ=0
Let Δ=b²-4ac

Δ=(1-5k)²-4*4k(k-1)

Δ=25k²-10k+1-16k²+16k

Δ=9k²+6k+1

And also Δ=0

So: 9k²+6k+1=0

We have a second equation but now our unknown value is k.
Let δ=b²-4ac

δ=6²-4*9*1

δ=36-36

δ=0

So because δ=0, there is an unic solution for this second equation.
k=-b/(2a)
k=-6/18
k=-1/3
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