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Question
If 3 is a root of the quadratic equation` x^2-x+k=0` find the value of p so that the roots of the equation `x^2+2kx+(k^2+2k+p)=0` are equal.
Solution
It is given that 3 is a root of the quadratic equation `x^2-x+k=0`
∴ `(3)^2-3+k=0`
⇒ `k+6=0`
⇒ `k=-6`
The roots of the equation` x^2+2kx+(k^2+2k+p)=0 ` are equal.
∴ `D=0`
⇒`(2k)^2-4xx1xx(k^2+2k+p)=0`
⇒` 4k^2-4k^2-8k-4p=0`
⇒`-8k-4p`
⇒`p=(8k)/-4=-2k`
⇒ p=`-2xx(-6)=12`
Hence, the value of p is 12.
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