North Carolina Math 3 EOC Chapter 5

1 pt

1.

According to the Rational Root Theorem, which of these is a possible rational root of the equation $2{x}^{3}+3{x}^{2}-23x-12=0$?

A

$x=\frac{1}{12}$

B

$x=\frac{1}{6}$

C

$x=\frac{1}{4}$

D

$x=\frac{1}{2}$

1 pt

2.

To find the roots of the equation ${x}^{3}-8{x}^{2}-3x+90=0$, all the possible rational roots were tested with the function $f\left(x\right)={x}^{3}-8{x}^{2}-3x+90$. Is $x=-3$ a root of the equation?

A

No, because $f(-3)\ne 0$.

B

No, because $f(-3)=0$

C

Yes, because $f(-3)\ne 0$.

D

Yes, because $f(-3)=0$

1 pt

5.

What is the solution to the equation ${x}^{3}+12{x}^{2}-2x-24=0$?

A

*x* = -12. -2*i*, and 2*i*

B

*x* = 12, $-\sqrt{2}$ and $\sqrt{2}$

C

*x* = -12. 2*i*, and 2*i*

D

*x* = 12, $-\sqrt{2}$ and $\sqrt{2}$

1 pt

6.

The graphs of the functions $f\left(x\right)={x}^{2}$ and $g\left(x\right)=3x+28$ intersect at the points ( –4, 16) and (7, 49). What is the solution to the equation ${x}^{2}=3x+28$?

A

*x* - = -4 and 16

B

*x* - = -4 and 7

C

*x* - = 7 and 49

D

*x* - = 16 and 49

1 pt

8.

The graph of the function $f\left(x\right)\hspace{0.17em}={x}^{3}+5{x}^{2}+2x-8$ is shown below. What is the solution to the equation ${x}^{3}+5{x}^{2}+2x-8=0$?

A

*x* = -4, 2, and 1

B

*x* = -4, -2, and 1

C

*x* = -2, -1, and 4

D

*x* = -2, 1, and 4