1.

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.

Answer» Since -4 is a root of `x^(2)+px-4=0`
Hence, (-4) will satisfy the equation.
Therefore, `(-4)^(2)+p(-4)-4=0`
`implies16-4p-4=0`
`implies-4p+12=0`
`implies-4p=-12`
`impliesp=3" "....(1)`
Given that `x^(2)+px+q=0` has coincident roots.
`:.D=b^(2)-4ac=0`
`impliesD=p^(2)-4xx1xxq=0`
`impliesp^(2)-4q=0`
`implies3^(2)-4q=0" "["form"(1)]`
`implies9-4q=0`
`implies-4q=-9`
`impliesq=(9)/(4)`
Hence, p=3 and `q=(9)/(4)`


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