Quadratic Equations
A quadratic equation is an equation of the form \(ax^2 + bx + c = 0\), where \(a \ne 0\).
There are two common methods to solve it:
1. Factorising – expressing the quadratic as a product of two binomials.
2. Using the quadratic formula – apply the formula when factorising is difficult or not possible.
\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Example
Example 1: Solve \(x^2 + 5x + 6 = 0\)
→ Factorise: \((x + 2)(x + 3) = 0\)
→ \(x = -2\) or \(x = -3\)
Example 2: Solve \(2x^2 + 3x - 2 = 0\)
→ Use formula: \(a = 2\), \(b = 3\), \(c = -2\)
→ \(x = \dfrac{-3 \pm \sqrt{3^2 - 4(2)(-2)}}{2(2)}\)
→ \(x = \dfrac{-3 \pm \sqrt{9 + 16}}{4} = \dfrac{-3 \pm \sqrt{25}}{4}\)
→ \(x = \dfrac{-3 + 5}{4} = \dfrac{1}{2}\), or \(x = \dfrac{-3 - 5}{4} = -2\)
Practice
Solve: \(4x^2 - 25 = 0\)
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