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Extra resources for Algebra II Essentials For Dummies (For Dummies (Math & Science))

Sample text

Using the quadratic formula for this example, you let a = 48, b = –155, and c = 125. Filling in the values and solving for x, you get Starting with the plus sign, the first solution is For the minus sign, you get . The fact that 28 Algebra II Essentials For Dummies you get fractions tells you that you could’ve factored the quadratic: 48x2 – 155x + 125 = (3x – 5)(16x – 25) = 0. Do you see where the 3 and 5 and the 16 and 25 come from in the answers? Investigating irrational solutions The quadratic formula is especially valuable for solving quadratic equations that don’t factor.

When x = –3, you get The solution x = –3 works. Checking x = –5, you get This solution works, too. Chapter 4: Rolling Along with Rational and Radical Equations 41 Both solutions working out is more the exception rather than the rule. Most of the time, one solution or the other works, but not both. And, unfortunately, sometimes you go through all the calculations and find that neither solution works in the original equation. You get an answer, of course (that there is no answer), but it isn’t very fulfilling.

When you have the proportion , the following are also true: ✓ ad and bc, the cross-products, are equal, giving you ad = bc. Chapter 4: Rolling Along with Rational and Radical Equations ✓ and , the reciprocals, are equal, giving 39 . ✓ You can divide out common factors both horizontally and vertically. Solve for x in the proportion: . First reduce across the numerators, and then reduce the left fraction: becomes becomes Now cross-multiply and solve the resulting quadratic equation: As usual, you need to check to be sure that you haven’t introduced any extraneous roots.

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