Problem 3 Choosing an Appropriate Method

Which method(s) would you choose to solve each equation? Explain your reasoning.

1. 3 x 2 − 9 = 0 3 x squared , minus 9 equals 0  Square roots; there is no x-term

2. x 2 − x − 30 = 0 x squared , minus , x minus 30 equals 0  Factoring; the equation is easily factorable

3. 6 x 2 + 13 x − 17 = 0 6 x squared , plus 13 x minus 17 equals 0  Quadratic formula, graphing; the equation cannot be factored

4. x 2 − 5 x + 3 = 0 x squared , minus 5 . x plus 3 equals 0  Quadratic formula, completing the square, or graphing; the coefficient of the x 2 x squared -term is 1, but the equation cannot be factored

5. − 16 x 2 − 50 x + 21 = 0 negative , 16 x squared , minus 50 x plus 21 equals 0  Quadratic formula, graphing; the equation cannot be factored easily since the numbers are large

✓ Got It?

3. Which method(s) would you choose to solve each equation? Justify your reasoning.
   1. x 2 − 8 x + 12 = 0 x squared , minus 8 . x plus 12 equals 0
   2. 169 x 2 = 36 169 x squared . equals 36
   3. 5 x 2 + 13 x − 1 = 0 5 x squared , plus 13 x minus 1 equals 0

Take Note Key Concept: Using the Discriminant

Discriminant	b 2 − 4 a c > 0 b squared , minus 4 . eh c greater than 0	b 2 − 4 a c = 0 b squared , minus 4 . eh c equals 0	b 2 − 4 a c < 0 b squared , minus 4 . eh c less than 0
Example	x 2 − 6 x + 7 = 0 x squared , minus 6 . x plus 7 equals 0 The discriminant is ( − 6 ) 2 − 4 ( 1 ) ( 7 ) = 8 , open negative 6 close squared . minus 4 open 1 close open 7 close equals 8 comma  which is positive.	x 2 − 6 x + 9 = 0 x squared , minus 6 . x plus 9 equals 0 The discriminant is ( − 6 ) 2 − 4 ( 1 ) ( 9 ) = 0 . open negative 6 close squared . minus 4 open 1 close open 9 close equals 0 .	x 2 − 6 x + 11 = 0 x squared , minus 6 . x plus 11 equals 0 The discriminant is ( − 6 ) 2 − 4 ( 1 ) ( 11 ) = − 8 , open negative 6 close squared . minus 4 open 1 close open 11 close equals negative 8 comma  which is negative.
Number of Solutions	There are two real-number solutions.	There is one real-number solution.	There are no real-number solutions.