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Quadratic Equation (Using Factorization)

Recent discussion in Level II session:

Instead of using the complex formula for solving a quadratic equation, sometimes factorization generates a solution much faster.

Consider the equation to be: 16x² − 24x + 9 = 0 (like ax² + bx + c = 0)

Step 1: Multiply a and c and find factors of a.c such that they add up to b.
In this example ac = 16 × 9 = 144
The factors of 144 that sum up as b (= −24) are −12 and −12.

Step 2: Rewrite the equation with b replaced by the sum of two factors,
    take GCF for the first two terms, and last two terms as below:
    => 16x² − 12x − 12x + 9 = 0
    => 4x(4x − 3) − 3(4x − 3) = 0

Step 3: Simplify the LHS expression as a product of two binomial factors and solve for x.
=> (4x − 3)(4x − 3) = 0
=> 4x − 3 = 0 or x = 3/4

Additional example: 4x² + 4x − 15 = 0
The solution set for this is, x = −5/2 or 3/2

Quadratic Equation (Using Factorization)

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