Class 10 Maths - Quadratic Equations

A Quadratic Equation in the variable $x$ is an equation of the form $ax^2 + bx + c = 0$, where $a \neq 0$.

1. Solution by Factorization

Finding two numbers whose product is $ac$ and sum is $b$. Then splitting the middle term.

2. The Quadratic Formula

For the equation $ax^2 + bx + c = 0$, the roots are given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

3. Nature of Roots

The term $D = b^2 - 4ac$ is called the Discriminant.

• If D > 0: Two distinct real roots.
• If D = 0: Two equal real roots.
• If D < 0: No real roots (Imaginary roots).

4. Word Problems

Quadratic equations are commonly used to solve real-life problems involving:

• Area of rectangles.
• Speed and time (Distance problems).
• Numbers and their squares.

✅ Important Points to Remember

1. A quadratic equation has at most two roots.
2. If the discriminant is a perfect square, the roots are rational.
3. Factorisation method is usually faster for simple integers.

Practice at least 20 problems on the Quadratic Formula! 📐