Question

Chintu is given a quadratic equation $a{x}^2+bx+c=0$ and is asked to make another quadratic equation from this with a = 1. Also, one root of the second quadratic equation is same as one of the roots of the first equation but opposite in sign and the other root of the second equation is two times the second root of the first equation. Find the percentage change in the constant term of the second equation as compared to the first equation?

• A. 200% increases
• B. 300% decrease
• C. 400% increase
• D. 100% decrease

Answer 1

The correct option is B 300% decrease

Let the equation be
$x^2-2x+1=0\dots \dots \left(1\right)$
Roots for the above quadratic equation are 1, 1
and $x^2-x-2=0\dots \dots \left(2\right)$
Roots for the above quadratic equation are -1, 2
Roots of both the equations satisfy the given conditions.
Hence, required percentage $=\frac{1-(-2)}{1}\times 100=300\%$