Question

• 4x³ + 9x² + 2x - 5 to complete these sentences.

= 2 is ______.

1. state all the intervals in which the zeros are located.

f(x) = x⁴ + 4x³ - 9x² - 37x - 24

Explanation:

Step1: Evaluate \( f(-5) \)

Substitute \( x = -5 \) into \( f(x) = x^4 + 4x^3 - 9x^2 - 37x - 24 \):

$$
LATEXBLOCK0
$$

Step2: Evaluate \( f(-4) \)

Substitute \( x = -4 \) into \( f(x) \):

$$
LATEXBLOCK1
$$

Step3: Evaluate \( f(-1) \)

Substitute \( x = -1 \) into \( f(x) \):

$$
LATEXBLOCK2
$$

Step4: Evaluate \( f(0) \)

Substitute \( x = 0 \) into \( f(x) \):

$$ f(0) = 0^4 + 4(0)^3 - 9(0)^2 - 37(0) - 24 = -24 $$

Step5: Evaluate \( f(3) \)

Substitute \( x = 3 \) into \( f(x) \):

$$
LATEXBLOCK3
$$

Wait, that can't be right. Wait, let's recalculate \( f(3) \):

$$
LATEXBLOCK4
$$

Wait, maybe I made[LLM SSE On Failure]

Answer:

Step1: Evaluate \( f(-5) \)

Substitute \( x = -5 \) into \( f(x) = x^4 + 4x^3 - 9x^2 - 37x - 24 \):

$$
LATEXBLOCK0
$$

Step2: Evaluate \( f(-4) \)

Substitute \( x = -4 \) into \( f(x) \):

$$
LATEXBLOCK1
$$

Step3: Evaluate \( f(-1) \)

Substitute \( x = -1 \) into \( f(x) \):

$$
LATEXBLOCK2
$$

Step4: Evaluate \( f(0) \)

Substitute \( x = 0 \) into \( f(x) \):

$$ f(0) = 0^4 + 4(0)^3 - 9(0)^2 - 37(0) - 24 = -24 $$

Step5: Evaluate \( f(3) \)

Substitute \( x = 3 \) into \( f(x) \):

$$
LATEXBLOCK3
$$

Wait, that can't be right. Wait, let's recalculate \( f(3) \):

$$
LATEXBLOCK4
$$

Wait, maybe I made[LLM SSE On Failure]