Question

The sum of the squares of the roots of the equation $x^2-9x+q=0$ is $53$. Then the value of $q$ is

• A. 14.00
• B. 14
• C. 14.0
• D. 014

Answer 1

Answer: (A), (B), (C), (D)

Given $x^2-9x+q=0$ and $a^2+b^2=53$ if $a$ and $b$ are its roots.
$\Rightarrow a+b=9,ab=q$

Using the identity $(a+b{)}^2=a^2+b^2+2ab$
$\Rightarrow (9{)}^2=53+2q$
$81=53+2q$
$\Rightarrow q=14$