Solving Quadratic Equations Easily

Introduction

Quadratic equations are common in mathematics and appear in many real-world applications such as engineering, finance, and physics.

What is a Quadratic Equation?

A quadratic equation has the form:

$ax^2+bx+c=0$ax2+bx+c=0

$a$a

$b$b

$c$c

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{0\pm\sqrt{16}}{2}\approx -2,\ 2$x=2a−b±b2−4ac​​=20±16​​≈−2, 2

where:

• a ≠ 0
• b and c are constants

Methods of Solving

Method 1: Factorization

Solve:

$x^2+5x+6=0$x2+5x+6=0

Factor:

(x + 2)(x + 3) = 0

Therefore:

• x = -2
• x = -3

Method 2: Quadratic Formula

Use:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$x=2a−b±b2−4ac​​

$a$a

$b$b

$c$c

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{0\pm\sqrt{16}}{2}\approx -2,\ 2$x=2a−b±b2−4ac​​=20±16​​≈−2, 2

Example:

2x² + 3x − 2 = 0

Substitute values and solve.

Common Mistakes

• Wrong signs
• Incorrect substitution
• Arithmetic errors

Study Tips

• Practice daily
• Memorize formulas
• Check answers by substitution

Conclusion

Mastering quadratic equations improves problem-solving skills and builds confidence in mathematics.