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  4. Sachin and Rahul attempted to solve a quadratic equaiton. 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 :

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Q. Sachin and Rahul attempted to solve a quadratic equaiton. 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 :

AIEEEAIEEE 2011Complex Numbers and Quadratic Equations

Solution:

Let the correct equation be $ax^2 + bx + c = 0$
$-\frac{b}{a} = 7\quad\quad........ \left(i\right)$
$\frac{c}{a} = 6\quad\quad........ \left(ii\right)$
from $\left(i\right)$ and $\left(ii\right)$
correct equation is
$x^{2} - 7x + 6 = 0$
roots are 6 and 1

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