Q. Two students while solving a quadratic equation in $x,$ one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term coefficient of $x^{2}$ correctly as $- 6$ and 1 respectively the correct roots are
A) $3,\ - 2$
B) $- 3,\ 2$
C) $- 6,\ - 1$
D) $6,\ - 1$
Explanation
(d)
Let the correct equation be $ax^{2} + bx + c = 0$ and the correct roots are $\alpha\ and\ \beta$. Taking $c$ wrong, the roots are 3 and 2.
$\therefore\ \ \alpha + \ \beta = 3 + 2 = 5$ ...(i)
Also, $a = 1\ and\ c = - 6$
$\therefore\ \alpha\beta = \frac{c}{a} = - 6$ ...(ii)
On solving Eqs.(i) and (ii), the correct roots are 6 and $- 1$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.