Question

Sum of the squares of the roots of the quadratic equation $x^2-5x+2=0$ is :

• A. 15
• B. 17
• C. 33
• D. 21

Answer 1

The correct option is D 21

The equation is $x^2-5x+2=0$

Then a=1 ,b=-5 and c=2

Then the sun of root =$\alpha +\beta =-\left(\frac{b}{a}\right)=-\left(\frac{-5}{1}\right)=5$

Product of root =$\alpha \beta =\frac{c}{a}=\frac{2}{1}=2$

$\therefore \alpha 2+{\beta }^2={(\alpha +\beta )}^2-2\alpha \beta \Rightarrow {\alpha }^2+{\beta }^2=(5{)}^2-2\times 2\Rightarrow {\alpha }^2+{\beta }^2=25-4=21$