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Thus far, we have solved quadratic equations by factoring and the method of completing the square Property. We have one more method to learn; it is the Quadratic Formula. The method can be used whenever the quadratic equation is not factorable. This formula is as follows:.
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Thus far, we have solved quadratic equations by factoring and the method of completing the square Property. We have one more method to learn; it is the Quadratic Formula. The method can be used whenever the quadratic equation is not factorable. This formula is as follows: The Quadratic Formula Before we get started, let’s practice simplifying some rational expressions. Factor out 2 from numerator then reduce. or shortcut: 3 4 Divide all terms by 2 2 3 2 Divide all terms by 6 1 No common factor.
Your Turn Problem #3 The first step is to identify a, b, and c by comparing to the standard form ax2 + bx + c = 0. Then, replace these numbers into the quadratic formula and simplify. Hint: since you need to memorize the formula, it is always a good idea to just write it down whenever you need to use it. The more times you write something down, it will help you to memorize whatever it is you need to memorize. 1. Write down the Q.F. and a, b and c. 2.Substitute a, b, and c into the Q.F. 3. Simplify
Solution: Your Turn Problem #4 1 1 3 1. Write down the Q.F. and a, b and c. 2.Substitute a, b, and c into the Q.F. 3. Simplify
Your Turn Problem #4 Note: Since the solutions are rational numbers, the quadratic equation was actually factorable. Solution: 1. Since this equation is not written in standard form, that will be our first step. Distribute on the LHS, then get a zero on the RHS. 2. Now we can write down the Q.F. and a, b and c. 3.Substitute a, b, and c into the Q.F. and simplify.
Solution: Your Turn Problem #5 1. Write down the Q.F. and a, b and c. 2.Substitute a, b, and c into the Q.F. 3. Simplify Whenever we have a complex number, it must be written in a+bi form.
The sum of the roots = , The product of the roots = Your Turn Problem #6 Check the solution to the quadratic equation using the sum and product check. The Sum and Product Check. In past equations, we would check our answer to verify the solution was correct. However it can be extremely difficult to do this. Fortunately, we have an alternative method for verifying the solutions. We have the following two relationships: Example 6. Check the solution to the quadratic equation using the sum and product check. (We solved this example earlier in this lesson.) 1st, find the sum of the roots. 2nd, find the product of the roots. Since these values match, our answers are correct. The End. B.R. 5-31-07
