Question

A and B solved a quadratic equation. In solving it , A made a mistake in the constant term and obtained the roots as 5, -3 while B made a mistake in the coefficient of x and obtained the roots as 1, -3. The correct roots of the equation are

• A. 1,3
• B. -1,3
• C. -1,-3
• D. 1,-1

Answer 1

The correct option is B

-1,3

Using the reverse gear approach
If the equation is $a{x}^2+bx+c=0.$
A's mistake will be in "c”, hence sum of roots = $-\frac{b}{a}=\mathrm{2.....}\left(i\right)$ will be the correct value. Product of roots = $\frac{c}{a}$ will be wrong in this case
B's mistake will be in "b”, hence product of roots =$\frac{c}{a}=-\mathrm{3......}\left(ii\right)$ will yield the correct value. In this case, sum of roots value = $-\frac{b}{a}$ will be wrong

Look in the answer options for the pair of roots which satisfy sum of roots = 2 and product of roots = -3. Answer is option (b).