Precalc0011to0016-page5

Precalc0011to0016-page5 - Then, ax 2 + bx + c Solutions to...

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(Section 0.11: Solving Equations) 0.11.5 Observe that the radicand b 2 ± 4 ac in the Quadratic Formula is the discriminant of ax 2 + bx + c . In Example 2, we saw that the discriminant of 2 x 2 ± 7 x ± 15 was 169, a perfect square , which allowed us to eliminate the radical sign and obtain rational numbers as solutions to 2 x 2 ± 7 x ± 15 = 0 . Also, by the Test for Factorability from Section 0.7, 2 x 2 ± 7 x ± 15 can be factored over the integers. In Example 3, we were able to solve 2 x 2 ± 7 x ± 15 = 0 using the Factoring Method, and we obtained rational numbers as solutions. Test for Factorability and Types of Solutions The Test for Factorability applies to ax 2 + bx + c , where a , b , and c are nonzero, integer coefficients. (Assume the GCF is 1 or ± 1 ; if it is not, factor it out.) If the discriminant b 2 ± 4 ac is …
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Unformatted text preview: Then, ax 2 + bx + c Solutions to ax 2 + bx + c = a perfect square can be factored (over the integers) two rational numbers in fact, 0 and is a PST (Perfect Square Trinomial) one rational number not a perfect square is prime (over the integers) and positive two irrational numbers and negative two imaginary numbers (see Chapter 2) If ax 2 + bx + c can be factored over the integers , then the Factoring Method is usually faster than the Quadratic Formula when solving ax 2 + bx + c = . However, if it is prime , then the Quadratic Formula is typically used. A method for factoring ax 2 + bx + c using the Quadratic Formula will be presented in Chapter 2....
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This document was uploaded on 12/29/2011.

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