CPM Homework Help : A2C Problem 11-104

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Home > A2C > Chapter Ch11 > Lesson 11.2.5 > Problem 11-104

11-104.

Without graphing, find where each of the following curves crosses the x-axis. (Find the exact points!)

$f \left(x\right) = x^{2} − x − 12$
Hint (a):
Factor.
f(x) = (x + 3)(x − 4)
Answer (a):
(−3, 0) and (4, 0)

$f \left(x\right) = 2x^{2} − 3x − 9$
Hint (b):
Use the quadratic formula.
Answer (b):
(−1.5, 0) and (3, 0)

$f \left(x\right) = 2x^{2} + x − 7$
Hint (c):
See part (b).

$f \left(x\right) = 3x^{2} − 2x + 7$
Hint (d):
See part (b).
Answer (d):
It does not intersect the x-axis.

$f \left(x\right) = 3x^{3} + 2x^{2} − 8x$
Hint (e):
x is a common factor.
More Help (e):
After you factor out x, factor or use the quadratic formula to find the roots of the rest.

$f \left(x\right) = 2x^{3} + 2x^{2} + 13x$
Hint (f):
See part (e).

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