There will be obstacles. There will be doubters. There will be mistakes. But with hard work, there are no limits. – Michael Phelps

# Quadratic Equations Class 10 Maths

In this chapter, you have studied the following points:

1. A quadratic equation in the variable x is of the form $ax^2+bx+c=0$, where a, b, c are real numbers and a ≠ 0.

2. A real number α is said to be a root of the quadratic equation $ax^2 + bx + c = 0$, if $aα^2+ bα + c = 0$. The zeroes of the quadratic polynomial $ax^2 + bx + c = 0$ and the roots of the quadratic equation $ax^2+ bx + c$

3. If we can factorise $ax^2+bx+c$, $a \ne 0$ into a product of two linear factors, then the roots of the quadratic equation $ax^2+bx+c$ can be found by equating each factor to zero.

4. A quadratic equation can also be solved by the method of completing the square.

5. Quadratic formula: The roots of a quadratic equation $ax^2+bx+c=0$ are given by $\frac{-b \pm \sqrt{b^2-4ac}}{2a}$, provided $b^2-4ac \ge 0$.

6. A quadratic equation $ax^2 + bx + c = 0$ has
(i) two distinct real roots, if $b^2 – 4ac > 0$,
(ii) two equal roots (i.e., coincident roots), if $b^2 – 4ac = 0$, and
(iii) no real roots, if $b^2– 4ac < 0$.