10th Class Mathematics Quadratic Equations Quadratic Equations

      Quadratic Equations

The most general quadratic equation is \[a{{x}^{2}}+bx+c=0\]. This equation can be solved by using the Discriminant method. In this method we find the discriminant of the given quadratic equation as follows:

\[D={{b}^{2}}-4ac,\]

(a) If D > 0, then the given equation will have real and distinct roots and we can find the roots of the given equation.

(b) If D = 0, then the given equation will have real and equal roots.

(c) If D < 0, then the given equation will have no real roots. In this case roots will be imaginary. Here we find the imaginary roots only.

In case of real roots we can find the roots by using the formula,

\[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}or\frac{-b\pm \sqrt{D}}{2a}\]

The quadratic equation can have maximum of two roots.

In case of imaginary roots we can find the roots by using the relation,

\[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}or\frac{-b\pm i\sqrt{D}}{2a}\]

Where, i denote the imaginary part of the roots.