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Quadratic Equations
Lesson 5
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Lesson 5: Quadratic Equation Methods

Interpret and solve quadratics with root structure.

Quadratic equations can be solved by factoring or formula. The roots reveal intercepts and shape information for graphs.

Key formula

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

Worked example

2x2+2x−84=0⇒x∈{−7,6}2x^2+2x-84=0\Rightarrow x\in\left\{-7,6\right\}

Checkpoint

Sum of roots for 3x2−15x−18=0 is ?\text{Sum of roots for }3x^2-15x-18=0\text{ is }?

Recap

  • - Discriminant determines root type.
  • - Factoring is fastest when integer roots exist.
  • - -b/a gives sum of roots quickly.
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