Question

For what value of k, are the roots of the quadratic equation (k - 4)x 2 + (k - 4)x + 4=0 equal?

Answer 1

Let α, β are the roots of  (k-4)x²+(k-4)x+4=0 -----------(1)
and α=β.
Now from the relations btween the roots and coefficients we get,
α+β=-(k-4)/(k-4)
or, α+α=-1
or, 2α=-1
or, α=-1/2
or, α²=1/4 -------------(2) and
αβ=4/(k-4)
or, α.α=4/(k-4)
or, α²=4/(k-4)
or, 1/4=4/(k-4)
or, 1=16/(k-4)
or, k-4=16
or, k=16+4
or, k=20 Ans.