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Definitions: Quadratic equation:
where a, b, c are constants.
Note: If a quadratic equation does not have a general form, we can always rewrite it into a general
Solving Quadratic Equations
We will only consider real number solutions .
Always modify the equation in general form first. Then use one of two methods :
2. The quadratic formula
If the given equation is a rational equation , check the values that make the denominator(s) zero so
that you can eliminate them from the solution.
Zero product property : ab = 0, where a, b are real a = 0 or b = 0 or both.
Ex.1 (#10) Solve
Ex.3 (#16) Solve (x - 3)(1 - x) = 1
Ex.4 (p.142) Solve
Ex.5 (#34) Solve
Quadratic Formula: If ax2 + bx + c = 0, where a ≠ 0, then
|Sign of b 2 - 4ac||Solutions|
| Two distinct real solutions
Exactly one real solution
No real solutions
Ex.6 (#22) Solve
Ex.7 (#24) Solve
Note: There may be solutions to a quadratic equation that are not the solutions to a problem.
Ex.8 (#44) If the pro t from the sale of x units of a product is what level(s) of
production will yield a pro t of $180?
Ex.9 (#48) A tennis ball is thrown into a swimming pool
from the top of a tall hotel. The height of the
ball from the pool is modeled by
where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown is it 4
feet above the pool?