SaiBook.us Algebra

Example

Title: Find the roots of the quadratic equation by factorization

Grade: 9-a Lesson: S1-L4

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

1. Find the roots of \$x^2 + x - 6 \$.

Step 1a

Given.

$1a$

Explanation: Given equation is \$x^2 + x = 6\$.

Step 1b

Rewrite the equation.

$1b$

Explanation: Rewrite the equation \$x^2 + x = 6\$ as \$x^2 + 3x - 2x - 6 = 0\$.

Step 1c

case-1:

$1c$

Explanation: Consider case-1:

⇒ \$x + 3 = 0\$
⇒ \$x = - 3\$

Step 1d

case-2:

$1d$

Explanation: Consider case-2:

⇒ \$x - 2 = 0\$
⇒ \$x = 3\$

Step 1e

From case-1 and case-2:

$1e$

Explanation: From case-1 and case-2:

⇒ \$x = - 3\$ or \$x = 2\$

∴ The roots of equation \$x^2 + x - 6 = 0\$ are \$x = - 3\$ or \$x = 2\$ .