Solving quadratic equations square root property quizlet

If the polynomial in the equation is not factorable, make it factorable by completing the square

Steps:
1. transform equation to: x^2 + bx = c
2. if a is not 1, divide both sides of equation by a
3. solve for the last term to form a PST and it to both sides of the equation
4. factor the PST and it to both sides of the equation
5. apply square root property

PST = perfect square trinomial

last term = ( coefficient of middle term / 2)^2

By knowing the value of the discriminant and applying the following rules:

1. If the disc is positive and a perfect square, then the square root symbol will go away in the simplifying process, thus yielding 2 rational solutions (because of the ±). This indicates that the quadratic equation is factorable. (Whenever the solution(s) are rational the quadratic equation is factorable over the integers). Ex: √16

2. If the disc is positive and not a perfect square, then the simplified solutions will contain square root symbols, therefore yielding 2 irrational solutions. These quadratic equations are not factorable over the integers. Ex: √20

3. If the disc is equal to 0, and √0 = 0, this yields 1 rational solution (-b/2a by the time everything is simplified). Since the solution is rational, the quadratic equation is factorable.

4. If the disc is negative, the quadratic equation will contain 2 complex solutions because simplifying will result in ± imaginary part. These quadratic equations are not factorable over the integers.

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