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Upon completing this section you should be able to: bx c = 0 when a ≠ 0 and a, b, and c are real numbers.All quadratic equations can be put in standard form, and any equation that can be put in standard form is a quadratic equation.The method of solving by factoring is based on a simple theorem. We will not attempt to prove this theorem but note carefully what it states.
In previous chapters we have solved equations of the first degree.
You now have the necessary skills to solve equations of the second degree, which are known as quadratic equations.
Upon completing this section you should be able to: From your experience in factoring you already realize that not all polynomials are factorable.
Therefore, we need a method for solving quadratics that are not factorable.
As already discussed, a quadratic equation has no real solutions if D A ball is thrown upwards from a rooftop, 80 m above the ground. 3) When the ball hits the ground, h = 0; -16t km upstream than to return downstream to the same spot.
It will reach a maximum vertical height and then fall back to the ground. The speed of the stream is: A) 6 km/h B) 5 km/h C) 3.5 km/h D) 4.5 km/h Solution: A) Let the speed of the stream be represented by x.
The task in completing the square is to find a number to replace the -7 such that there will be a perfect square.
Consider this problem: Fill in the blank so that "x 6x _______" will be a perfect square trinomial.
Note that in this example we have the square of a number equal to a negative number.
This can never be true in the real number system and, therefore, we have no real solution.