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Question

If 4 is a root of the quadratic equation x2+px4=0 and the quadratic equation x2+px+k=0 has equal roots, find the value of p and k.

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Solution

It is given that -4 is a root of the equation x2+px4=0.
Then, -4 must satisfy the equation,
(4)2+p×(4)4=0
164p4=0
4p=12
p=3
Now, the equation x2+px+k=0 has equal roots
Therefore,
Discriminant, D=0b24ac=0
p24k=0
94k=0
k=94

Therefore, p=3 and k=94.

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