Question

If $p\epsilon Q$ and the quadratic equations $x^2-4x+1=0$ and $p{x}^2-(p^2+3)x+2p^2-p=0$ have a root in common, then the value(s) of $p$ are

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is A $1$

Roots of the equation $x^2-4x+1=0$ are $2\pm \sqrt{3}$

Both the roots of the above equation are imaginary

Now second equation has common root

If $(2+\sqrt{3})$ is a common root $\Rightarrow$ other root must be $2-\sqrt{3}$ and vice verse as coefficients of second equation are real

As coefficients are real it has conjugate roots ie, it cannot have one imaginary root and one real root

$\therefore$two equations are identical

Comparing coefficients of 2 equations we get $p=1$