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If -4 is a root of the equation x^(2)+px...

If -4 is a root of the equation `x^(2)+px-4=0` and the equation `x^(2)+px+q=0` has coincident roots, find the values of p and q.

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Since -4 is a root of the equation `x^(2)+px-4=0,` we have
Now, the roots of `x^(2)+px+q=0` being equal, we have
`p^(2)-4q=0implies3^(2)-4q=0implies4q=9impliesq=(9)/(4).`
Hence, p=3 and `q=(9)/(4).`
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