ITM 107 Lecture Notes - Lecture 9: Quadratic Formula, Xterm, Social Security Trust Fund
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LECTURE 7 QUADRATIC AND OTHER SPECIAL FUNCTIONS
• A quadratic equation in one variable is an equation that can be written in the general
• where a, b, and c represent constants. For example, the equations
are quadratic equations.
• When we solve quadratic equations, we will be interested only in real number solutions
and will consider two methods of solution: factoring and the quadratic formula.
• Solution by factoring is based on the following property of the real numbers.
• Zero Product Property
• Hence, to solve by factoring, we must first write the equation with zero on one side.
Example – Solving by Factoring
a) Note that the left side of the equation is factored, but the right member is
not 0. Therefore, we must multiply the factors before we can rewrite the
equation in general form.
b) The LCD of all fractions is x (3x + 6). Multiplying both sides of the equation by
this LCD gives a quadratic equation that is equivalent to the original equation
for x ≠ 0 and x ≠ –2. (The original equation is undefined for these values.)