Quadratics With Irrational Solutions
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4Regents Exam Questions
Name: ________________________
A2.A.25: Quadratics with Irrational Solutions
A2.A.25: Quadratics with Irrational Solutions: Solve quadratic equations, using the quadratic
formula
2
2
1 The solutions of the equation y
− 3y = 9 are
4 Solve the equation 6x
− 2x − 3 = 0 and express the
answer in simplest radical form.
3 ± 3i
3
1)
2
3 ± 3i
5
2)
2
5 Barb pulled the plug in her bathtub and it started to
−3 ± 3
5
3)
drain. The amount of water in the bathtub as it
2
drains is represented by the equation
3 ± 3
5
4)
2
− 8t + 120 , where L represents the number
L = −5t
2
of liters of water in the bathtub and t represents the
amount of time, in minutes, since the plug was
pulled. How many liters of water were in the
bathtub when Barb pulled the plug? Show your
2
reasoning. Determine, to the nearest tenth of a
2 The roots of the equation 2x
+ 7x − 3 = 0 are
minute, the amount of time it takes for all the water
1
1)
and −3
−
in the bathtub to drain.
2
1
2)
and 3
2
−7 ±
73
3)
4
6 A homeowner wants to increase the size of a
7 ±
73
rectangular deck that now measures 15 feet by 20
4)
4
feet, but building code laws state that a homeowner
cannot have a deck larger than 900 square feet. If
the length and the width are to be increased by the
same amount, find, to the nearest tenth, the
maximum number of feet that the length of the
3 A cliff diver on a Caribbean island jumps from a
deck may be increased in size legally.
height of 105 feet, with an initial upward velocity
of 5 feet per second. An equation that models the
height, h(t) , above the water, in feet, of the diver in
time elapsed, t, in seconds, is
2
h(t) = −16t
+ 5t + 105 . How many seconds, to the
nearest hundredth, does it take the diver to fall 45
feet below his starting point?
1)
1.45
2)
1.84
3)
2.10
4)
2.72
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