Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are:

6, 1

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4, 3

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-6, -1

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-4, -3

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Solution

The correct option is A 6, 1
Let $a x^{2} + b x + c = 0$ be the correct equation.
Sachin's equation: $a x^{2} + b x + c^{'} = 0$ has roots (4,3)
Rahul's equation: $a x^{2} + b^{'} x + c = 0$ has roots (3,2)
Therefore, $- \frac{b}{a} = 7$ and $\frac{c}{a} = 6$ Or, $b = - 7 a$ and $c = 6 a$
So, the correct equation is : $a x^{2} - 7 a x + 6 a = 0$ Or, $x^{2} - 7 x + 6 = 0$ Its roots are 6,1.

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