Question

Rohan and Sohan were attempting to solve the quadratic equation, $x^2-a x+b=0$. Rohan copied the coefficient of $x$ wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3 . Find the correct roots.

• A. -2 and -24
• B. 2 and 24
• C. 4 and 12
• D. -4 and -12

Answer 1

Answer: (D)

Rohan copied only the coefficient of $x$ wrongly.
$\therefore$ He must have copied the constant term correctly.
$\therefore \text { Correct product of the roots }=\frac{b}{1}=4(12)$
$\Rightarrow b=48$
Sohan copied only the constant term wrongly.
$\therefore$ He must have copied the coefficient of $x$ correctly.
$\therefore$ Correct sum of the roots $=a=-19+3=-16$
Correct equation is $x^2-(-16) x+48=0$
$\Rightarrow x^2+16 x+48=0$
$\Rightarrow(x+4)(x+12)=0$
$\Rightarrow x=-4 \text { or }-12 $
$\therefore \text { Correct roots are }-4 \text { and }-12$