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For a particular value of $k$, one root of the equation $5x^2 + kx = 4$ is $x=2.$ What is the other root?

 May 30, 2020
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We have the equation: \(5x^2+kx=4\) we also know that one root is 2. This means that if we plug in 2 for x the equation should be satisfied.

If we do that we get: \(5(4)+2k=4\) this is simplified to \(k=-8\).

 

We now plug in the value of k and get: \(5x^2-8x=4\) or \(5x^2-8x-4=0\).

 

Factoring the quadratic (use the fact that we know that 2 is a root to make it easier) gives us \((x-2)(5x+2)\)

 

The other root is: \(\boxed{-5/2}\)

 

Hope you can understand this. :P

 May 31, 2020

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