Question

The value of $p$ in the equation $x^2-4x+p=0,$ if it is known that the sum of the squares of its roots is equal to $16$ is

• A. $4$
• B. $1$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

If $a$ and $b$ are the roots of the equation $x^2-4x+p=0$ then,
$(a+b)=4$ and $(a\cdot b)=p$
Now we know that the sum of squares of the roots is equal to $16$
$\Rightarrow a^2+b^2=16$
Since $(a+b{)}^2=a^2+b^2+2\cdot ab$
$\Rightarrow (a+b{)}^2-2\cdot ab=16$
$\Rightarrow (4{)}^2-2\cdot p=16$
$\Rightarrow 16-2\cdot p=16$
$\Rightarrow p=0$