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. 

 

Answer 1

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.