### Home > A2C > Chapter 11 > Lesson 11.2.5 > Problem11-104

11-104.

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

1. $f \left(x\right) = x^{2} − x − 12$

Factor.
f(x) = (x + 3)(x − 4)

(−3, 0) and (4, 0)

1. $f \left(x\right) = 2x^{2} − 3x − 9$

(−1.5, 0) and (3, 0)

1. $f \left(x\right) = 2x^{2} + x − 7$

See part (b).

1. $f \left(x\right) = 3x^{2} − 2x + 7$

See part (b).

It does not intersect the x-axis.

1. $f \left(x\right) = 3x^{3} + 2x^{2} − 8x$

x is a common factor.

After you factor out x, factor or use the quadratic formula to find the roots of the rest.

1. $f \left(x\right) = 2x^{3} + 2x^{2} + 13x$

See part (e).