NIELIT 2019 Feb Scientist C - Section C: 23

Question

Vidya and Vandana solved a quadratic equation. In solving it, Vidya made a mistake in the constant term and got the roots as $6$ and $2$, while Vandana made a mistake in the coefficient of $x$ only and obtained the root as $-7$ and $-1$. The correct roots of the equation are:

• A. $6,-1$
• B. $-7,2$
• C. $-6,-2$
• D. $7,1$

Answer 1

Answer is D

When there is no mistake in a and b, the sum of roots ($-\frac{b}{a}$) must be correct.

When there is no mistake in a and c, product of the roots ($\frac{c}{a}$) must be correct.

Therefore sum of roots = 6+2 = 8 and product of roots -7*-1 = 7

So the correct equation is $x^{2}-8x+7=0$     

(x-7) (x-1). The roots are 7, 1