Question

If a, b are the two roots of a quadratic equation such that $a+b=24$ and $a-b=8$, then the quadratic equation having a and b as its roots is:

• A. $x^2+2x+8=0$
• B. $x^2-4x+8=0$
• C. $x^2-24x+128=0$
• D. $2x^2+8x+9=0$

Answer 1

The correct option is C $x^2-24x+128=0$

$a+b=24,a-b=8$

Solving above equations simultaneously,

$\Rightarrow a=16,b=8$
$\therefore ab=128$
$\therefore$ Required equation is the one whose sum of the roots is $24$ and product of the roots is $128$.
i.e., $x^2-24x+128=0$