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Quadratic Equations
Example 11

Example 11: Quadratic Equation Methods

Step-by-step worked example for this lesson track.

Problem

Sum of roots for x2−x−12=0 is ?\text{Sum of roots for }x^2-x-12=0\text{ is }?

1. Recognize Pattern

x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

2. Apply Method

3x2−30x+72=0⇒x∈{4,6}3x^2-30x+72=0\Rightarrow x\in\left\{4,6\right\}

3. Conclude

r1+r2=−ba=1r_1+r_2=-\frac{b}{a}=1

Final answer

r1+r2=−ba=1r_1+r_2=-\frac{b}{a}=1
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