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algebra

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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.

Feb 24, 2021

#1
+602
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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 $7^2-4*7*k=0 \implies 49=28k\implies k=\boxed{\frac{7}{4}}$.

Feb 24, 2021
#2
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yes just like that

Feb 24, 2021