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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

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B

8, 5

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C

–8, –5

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D

8, -5

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Solution

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 = ba

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

Step 4:-
Thus product of roots = 10×4 = 40 = ca

Step 5:- Thus, the correct quadratic equation is x213x+40=0

x28x5x+40=0
x(x8)5(x8)=0
(x8)(x5)=0

So, the roots are 8, 5.


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