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Quiz 6
KEY
For questions 1-3, solve by the method indicated. If you cannot do so, you can solve by any method for 1.5
pts instead of 3pts each.
1.
(3 pts ) Solve for x by factoring.
x2
=
−3x + 4
x + 3x − 4
=
0
(x + 4) (x − 1)
=
0
x = −4
or
x=1
2
2.
(3 pts ) Solve for x by using the square root property.
9x2 − 25
=
9x2
=
x2
x
0
25
25
=
9r
= ±
= ±
3.
5
3
(3 pts ) Solve for x by completing the square.
x2 + 4x − 3
=
0
x2 + 4x
=
3
x + 4x + 4
=
3+4
2
=
7
x+2
=
2
(x + 2)
x
4.
25
9
(1 pt ) The quadratic formula is
√
± 7
= −2 ±
√
7
√
b2 − 4ac
.
2a
What is the discriminant and what is one thing it can tell us?
x=
−b ±
The discriminant is b2 − 4ac and it tells us how many solutions to the quadratic equation we
have. It also tells us what type of numbers these solutions will be.
5.
(3 pts ) Solve for x.
√
√
6.
x+2
2
x+2
=
4
=
42
x+2
=
16
x =
14
(3 pts ) Solve for x.
x4 + 4x2 − 12
=
0
u
=
x2
u2
=
x4
(u + 6) (u − 2)
=
0
u = −6
or
u=2
x2 = −6
√
x = ±i 6
7.
x2 = 2
√
x=± 2
(4 pts ) The daily price-demand equation for hamburgers at a fast-food restaurant is
q = 1, 600 − 200p
where q is the number of hamburgers sold daily and p is the rice of one hamburger (in dollars). Find the
and revenue when the price of a hamburger is $3. Recall the revenue equation: R = p · q .
demand
q
R
Extra Credit
=
1600 − 200 (3)
=
1600 − 600
=
1000
=
3 · 1000
=
3000
(1 pt ) The sum of a number and its reciprocal is 13/6. Find all such numbers.
1
x
=
x2 + 1
=
x+
Then solve using your favorite technique to get x =
13
6
13
x
6
3
2
or 23 .