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. 14.0
• B. 014
• C. 14
• D. 14.00

Answer 1

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

Given: $x^2-9x+q=0$
Let $a,b$ be the roots of the equation
$\Rightarrow a^2+b^2=53\cdots \left(i\right)$
$\&\Rightarrow a+b=9\cdots \left(ii\right),ab=q\cdots \left(iii\right)$
Now, Using the identity $(a+b{)}^2=a^2+b^2+2ab$
$\Rightarrow (9{)}^2=53+2q$
$\Rightarrow 81=53+2q$
$\Rightarrow q=14$