Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 7
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419-5 Solving Quadratic Equations by Using the Quadratic Formula
The discriminant is 41.
Since the discriminant is positive, the equation has two real solutions.
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13. 9x
+ 24x = −16
SOLUTION:
Write the equation in standard form.
For this equation, a = 9, b = 24, and c = 16.
The discriminant is 0.
Since the discriminant is 0, the equation has one real solution.
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14. 3x
− x = 8
SOLUTION:
Write the equation in standard form.
For this equation, a = 3, b = –1, and c = –8.
The discriminant is 97.
Since the discriminant is positive, the equation has two real solutions.
15. TRAMPOLINE Eva springs from a trampoline to dunk a basketball. Her height h in feet can be modeled by the
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equation h = –16t
+ 22.3t + 2, where t is time in seconds. Use the discriminant to determine if Eva will reach a
height of 10 feet. Explain.
SOLUTION:
Write the equation in standard form.
For this equation, a = –16, b = 22.3, and c = –8.
The discriminant is −14.91.
Since the discriminant is negative, the equation has no real solutions. Thus, Eva will not reach a height of 10 feet.
Solve each equation by using the Quadratic Formula. Round to the nearest tenth if necessary.
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16. 4x
+ 5x − 6 = 0
SOLUTION:
For this equation, a = 4, b = 5, and c = –6.
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