Question

Ganesh and Lokesh solved a quadratic equation. In solving it, Ganesh made a mistake in the constant term and got the roots as 6 and 7, while Lokesh made a mistake in the coefficient of x only and obtained the roots as 4 and 10. The correct roots of the equation are:

• A. -8, 5
• B. 8, 5
• C. –8, –5
• D. 8, -5

Answer 1

The correct option is B

8, 5

Step 1:- Ganesh made mistake in constant term only,

Thus the sum of the roots was correct.

Step 2:- Sum of roots = 6 + 7 = 13 = $-\frac{b}{a}$

Step 3:- Lokesh made mistake only in the coefficient of $x$. So the product of roots was correct.

Step 4:-
Thus product of roots = 10$\times$4 = 40 = $\frac{c}{a}$

Step 5:- Thus, the correct quadratic equation is $x^2–13x+40=0$

$\Rightarrow x^2-8x-5x+40=0$
$\Rightarrow x(x-8)-5(x-8)=0$
$\Rightarrow (x-8)(x-5)=0$

So, the roots are 8, 5.