Question

Find the values of k for which the roots of the equation (k + 4)x 2 + (k + 1)x + 1 = 0 are real and equal.

Answer 1

roots are real and equal when,
D=b^2-4ac=0
now use this concept
=>(k + 1)^2 - 4 (k + 4).1=0

=>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

=> k=-3, 5

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