Question

The set of all real values of $p$ for which the equation $x+1=\sqrt{px}$ has exactly one root is

• A. {0}
• B. {4}
• C. {0, 4}
• D. {0,2}

Answer 1

The correct option is C {0, 4}

The equation can be written as $x^2+(2-p)x+1$

The equation will have exactly 1 root if the equation is a perfect square,

$⟹b^2-4ac=0$

$⟹(2-p{)}^2-4=0$

$⟹|2-p|=2$

$⟹2-p=2$ or $2-p=-2$,

$p=0,4$