Given that x = -5 is a root to the quadratic 2x^2 + px - 15 = 0, and the quadratic equation p(x^2 + x) + k = 0 has equal roots, find k.
+605 Putting $x=-5$, $50-5p-15=0\implies 5p=35\implies p=7$.
So $7(x^2+x)+k=0$ has equal roots. Let's expand: $7x^2+7x+k=0$ has equal roots. The discriminant is, therefore, $0$, so we have $7^2-4*7*k=0 \implies 49=28k\implies k=\boxed{\frac{7}{4}}$.
