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Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

 Jun 22, 2024
 #1
avatar+1075 
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First, let's combine all our like terms. We have

\(x^2+15x+k\)

 

There are many possibilities for what k may be. 

As long as two factors of k add up to 15, we are good. 

 

Examples are such as

\(k=14; x^2+15x+14 = (x+14)(x+1)\\ k=56; x^2+15x+56=(x+7)(x+8)\)

 

k can also be negative, such as

\(k=-100; x^2+15x-100 = (x+20)(x-5)\)

 

Thanks! :)

 Jun 22, 2024

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