Question

The quadratic equation whose roots are the sum and difference of the squares of roots of the equation $x^2-3x+2=0$ is

• A. $x^2+8x+15=0$
• B. $x^2-8x-15=0$
• C. $x^2+8x-15=0$
• D. $x^2-8x+15=0$

Answer 1

The correct option is D $x^2-8x+15=0$

Given equation is $x^2-3x+2=0$
$\Rightarrow (x-2)(x-1)=0$
$\Rightarrow x=1,2$
Therefore, the roots of the equation are $1$ and $2$.
Sum of the squares of the roots $\Rightarrow 1+4=5$
Difference of the squares of the roots $\Rightarrow 4-1=3$
Hence, the roots of the new equation are $5$ and $3$.
Therefore, the new quadratic equation is $x^2-8x+15=0$
[$\because$ sum$\Rightarrow 5+3=8$ and product$\Rightarrow \left(5\right)\left(3\right)=15$]