Quadratic Problem Solving

Quadratic Problem Solving-51
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.In previous chapters we have solved equations of the first degree.

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.In previous chapters we have solved equations of the first degree.

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In other words, the standard form represents all quadratic equations.

The solution to an equation is sometimes referred to as the root of the equation.

Step 1 If the coefficient of x2 is not 1, divide all terms by that coefficient.

Step 2 Rewrite the equation in the form of x2 bx _______ = c _______.

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.

Of course, both of the numbers can be zero since (0)(0) = 0. The solutions can be indicated either by writing x = 6 and x = - 1 or by using set notation and writing , which we read "the solution set for x is 6 and - 1." In this text we will use set notation.

- 10 = 0 is an incomplete quadratic, since the middle term is missing and therefore b = 0.

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.

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