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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.

 Jun 18, 2022
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Plug in \(x = -5\) into the first equation. Because it is a root, this equation will be true. 

 

Solving for p gives us: \(p = 7\)

 

Now, plugging this in the second equation gives us: \(7x^2 + 7x + k = 0 \)

 

For the equation to have 1 solution, the discriminant must equal 0. 

 

Can you take it from here?

 Jun 19, 2022

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