PrepTap
If the square of the sum of the roots of a quadratic equation is less than their product, the roots are
A. Even
B. Odd
C. Negative
D. Not real
E. Can’t say
This question is a part of the series of original questions posted by PrepTap. Follow us to receive more questions like this.This question deals with imaginary numbers, which i snot exactly tested in GMAT.
But let us see what does the question hold.
Let the roots of an equation \(ax^2+bx+c\) be \(x_1\) and \(x_2\).
Sum of roots = \(x_1 + x_2 = -\frac{b}{a}....(x_1+x_2)^2=\frac{b^2}{a^2}\)
Product of roots = \(x_1 * x_2 = -\frac{c}{a}\)
Now given => \((x_1+x_2)^2<x_1*x_2.........\frac{b^2}{a^2}<\frac{c}{a}.....b^2<ac....b^2-ac<0\)
\(b^2-ac\) is nothing but the discriminant, which tells us about the type of roots......
D>0...Two real roots
D=0....One real root
D<0...2 Imaginary roots
Since \(D=b^2-ac<0\), we have two complex roots or not real roots
D