Question

What is the nature of the roots of a quadratic equation?

Answer 1

Write the nature of the roots of a quadratic equation.

The general form of the quadratic equation is given by $a{x}^2+bx+c$, where $a,b,c$ are real numbers and $x$ is an unknown variable.

The discriminant of the quadratic equation is $D=b^2-4ac$.

The nature of the roots of a quadratic equation:

1. .If $D=0$, the roots are equal and real.
2. If $D<0$ , the roots are imaginary and unequal.
3. If $D>0$, the roots are real and unequal.
4. If $D>0$ and $D$ is a perfect square, the roots are real, rational, and unequal
5. If $D>0$ and $D$ is not a perfect square, the roots are real, irrational, and unequal
6. If $D>0$, $D$ is a perfect square, $a=1$ and $b$ and $c$ are integers, the roots are integral.

Hence, the nature of the roots is described.