INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Solving Equations Using the Quadratic Formula

• If you do not see an easy way to factor a quadratic equation, use the formula.
• The discriminant is the radicand in the Quadratic Formula. Use it to determine the number of real roots of a particular quadratic equation.
• If the discriminant is positive, the equation has 2 real roots.
• If the discriminant is 0, it has one rational root.
• If the discriminant is negative, it has no real roots.

### Solving Equations Using the Quadratic Formula

5j2 + 6j + 1 = 0
• j = [( − 6 ±√{62 − 4( 5 )( 1 )} )/2(5)]
• j = [( − 6 ±√{16} )/10]
j = − [1/5], − 1
8a2 − 11a + 3 = 0
• a = [( − ( 11 ) ±√{( 11 )2 − 4( 8 )( 3 )} )/2( 8 )]
• a = [( − ( 11 ) ±√{25} )/16]
• a = [(11 ±5)/16]
a = 1,[3/8]
b2 + 12b − 30 = 0
• b = [( − 12 ±√{122 − 4( 1 )( 30 )} )/2(1)]
b = [( − 12 ±√{24} )/2]
9r2 = 14r − 3
• 9r2 − 14r + 3 = 0
• r = [( − ( − 14 ) ±√{( − 14 )2 − 4( 9 )( 3 )} )/2( 9 )]
r = [(14 ±√{88} )/18]
4s2 = − 7s − 2
• 4s2 + 7s + 2 = 0
• s = [( − 7 ±√{72 − 4( 4 )( 2 )} )/2( 4 )]
s = [( − 7 ±√{17} )/8]
20m2 = 25m − 5
• 4m2 = 5m − 1
• 4m2 − 5m + 1 = 0
• m = [( − ( − 1 ) ±√{( − 5 )2} − 4( 4 )( 1 ))/2(4)]
• m = [(1 ±√9 )/8]
• m = [(1 ±3)/8]
m = [1/2],[1/4]
14y2 = 49y + 21
• 2y2 = 7y + 3
• 2y2 − 7y − 3 = 0
• y = [( − ( − 7 ) ±√{( − 7 )2 − 4( 2 )( − 3 )} )/2( 2 )]
y = [(7 ±√{73} )/4]
54n2 = − 81n + 18
• 6n2 = 9n + 2
• 6n + 9n − 2 = 0
• n = [( − 9 ±√{92 − 4( 6 )( − 2 )} )/2( 6 )]
n = [( − 9 ±√{129} )/12]
Determine the number of real roots of 11x2 + 6x + 7 = 0D = 62 − 4( 11 )( 7 )
• D = 36 − 308
• D = − 272
No real solutions
b2 + 12b − 30 = 0
• b = [( − 12 ±√{122 − 4( 1 )( 30 )} )/2( 1 )]
b = [( − 12 ±√{24} )/2]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Solving Equations Using the Quadratic Formula

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