Quadratic Equations: Factoring

Recall that if a product of two factors is equal to zero, then at least one of the factors must be equal to zero:
  1. If $ab=0$, then either $a=0$ or $b=0$.
We can use this important rule to solve quadratic equations:
  1. Rewrite your quadratic equation in standard form: $ax^{2}+bx+c=0$.
  2. If possible, factor the quadratic expression on the left side of the equation. If the expression is not factorable, try a different technique.
  3. Set each factor equal to zero and solve the resulting linear equation for $x$.
Quadratic equations: factoring.

The Quadratic Formula

You should have the quadratic formula memorized. If $ax^{2}+bx+c=0$, where $a \neq 0$, then all real-valued solutions are given by $$ x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}. $$ The expression $b^{2}-4ac$ is called the discriminant. Recall:
  1. $b^{2}-4ac > 0$ implies the quadratic equation has two solutions.
  2. $b^{2}-4ac = 0$ implies the quadratic equation has one solution.
  3. $b^{2}-4ac < 0$ implies the quadratic equation has no solutions. In this case the quadratic expression $ax^{2}+bx+c$ does not factor over the real numbers and is called an irreducible quadratic.
Quadratic equations: quadratic formula

Problem Set 2.3

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