Question

For what values of k, the roots of the quadratic equation (k + 4) x2 + (k+ 1)x + 1 = 0 are equal?

Answer 1

for having equal roots D should be equal to zero.
D=b^2-4×a×c
0 = (k+1)^2 - 4×(k+4)×1
(k^2 + 2k +1)- (4k +16) =0
k^2-2k-15 = 0
k^2 - 5k +3k- 15 = 0
k(k-5) + 3(k-5) = 0
(k+3)×(k-5)= 0

as product of two numbers is zero, so either one of them has to be zero.
k+3=0. or. k-5=0

therefore the values of k are -3 or 5.

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