Problem Solving Quadratic Equations Examples

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The method needed is called "completing the square." First let us review the meaning of "perfect square trinomial." When we square a binomial we obtain a perfect square trinomial.

The general form is (a b) The -7 term immediately says this cannot be a perfect square trinomial.

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.

We can never multiply two numbers and obtain an answer of zero unless at least one of the numbers is zero.

When you encounter an incomplete quadratic with c - 0 (third term missing), it can still be solved by factoring.

Notice that if the c term is missing, you can always factor x from the other terms.The height of the ball from the ground at time t is h, and is given by h = -16t 64t 80. Therefore, the speed of the motorboat upstream is (18 – x) km/h and the speed of the motorboat downstream is (18 x) km/h. Solution: 1) The given equation is h = -16t 144 Now for h to be maximum, the negative term should be minimum.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.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 quadratic formula can also be used to solve quadratic equations whose roots are imaginary numbers, that is, they have no solution in the real number system. All skills learned lead eventually to the ability to solve equations and simplify the solutions.From the two conditions for a perfect square trinomial we know that the blank must contain a perfect square and that 6x must be twice the product of the square root of x At this point, be careful not to violate any rules of algebra.For instance, note that the second form came from adding 7 to both sides of the equation.


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