Find value of $k$

Question

For what value of $k$, are the roots of the quadratic equation $$(k+4)x^2 + (k+1)x +1 = 0$$ equal.

Answer 1

Roots are equal, when the discriminant of this quadratic equation is zero.

$D = (k+1)^2-4(k+4)$

$0 = (k+1)^2-4(k+4) = k^2 - 2k - 15$

there are two solutions: $k = -3$ and $k = 5$