3.6 Solving Quadratic Equations

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Presentation transcript:

3.6 Solving Quadratic Equations By Finding the Square Root

Simplifying Expressions with Radicals Perfect Square can’t be in radical Fraction can’t be in radical Radical can’t be in the denominator Rationalize the denominator To add/subtract, you must have like radicands

EXAMPLE 1 Use properties of square roots Simplify the expression. a. 80 5 16 = 5 = 4 b. 6 21 126 = 9 14 = = 3 14 c. 4 81 = 4 81 = 2 9 d. 7 16 = 7 16 = 4 7

GUIDED PRACTICE GUIDED PRACTICE 27 10 15 9 64 ANSWER ANSWER ANSWER 3 8 3 6 5 8 28 15 4 98 ANSWER 2 15 ANSWER ANSWER 14 4 2 7 36 49 11 25 7 6 5 11

EXAMPLE 2 Rationalize denominators of fractions. 5 2 3 7 + 2 Simplify (a) and (b) SOLUTION = 3 7 + 2 7 – (a) 5 2 = 5 2 (b) 3 7 + 2 = 5 2 = 21 – 3 2 49 – 7 + 7 – 2 2 10 = = 21 – 3 2 47

Key to solving using square roots Remember—You have to include the positive (principle) root as well as the negative root. x2 = 121 x = ± 11

Solve a quadratic equation EXAMPLE 3 Solve a quadratic equation Solve 3x2 + 5 = 41. 3x2 + 5 = 41 Write original equation. 3x2 = 36 Subtract 5 from each side. x2 = 12 Divide each side by 3. x = + 12 Take square roots of each side. x = + 4 3 Product property x = + 2 3 Simplify.

Solve a quadratic equation EXAMPLE 3 Solve a quadratic equation ANSWER The solutions are and 2 3 2 3 – Check the solutions by substituting them into the original equation. 3x2 + 5 = 41 3x2 + 5 = 41 3( )2 + 5 = 41 2 3 ? 3( )2 + 5 = 41 – 2 3 ? 3(12) + 5 = 41 ? 3(12) + 5 = 41 ? 41 = 41  41 = 41 

Standardized Test Practice EXAMPLE 4 Standardized Test Practice SOLUTION 15 (z + 3)2 = 7 Write original equation. (z + 3)2 = 35 Multiply each side by 5. z + 3 = + 35 Take square roots of each side. z = –3 + 35 Subtract 3 from each side. The solutions are –3 + and –3 – 35

GUIDED PRACTICE GUIDED PRACTICE Simplify the expression. 6 5 19 21 5 30 399 21 ANSWER ANSWER 9 8 – 6 7 – 5 2 4 3 – 21 – 3 5 22 ANSWER ANSWER 17 12 2 4 + 11 51 6 ANSWER 8 – 2 11 5 ANSWER

GUIDED PRACTICE – 1 9 + 7 – 9 + 7 74 ANSWER 4 8 – 3 32 + 4 3 61 ANSWER

GUIDED PRACTICE Solve the equation. 5x2 = 80 ANSWER + 4 z2 – 7 = 29 + 6 ANSWER 3(x – 2)2 = 40 120 3 2 + ANSWER