A graph of the function g (x) = x^4-8x³+x²+42x has zeros at - 2, 0, 3 and 7. What are the signs of the values between 0 and 3? Show algebraically how you know.

Question

Mathematics

Sylvia Goodman

4 December, 02:22

A graph of the function g (x) = x^4-8x³+x²+42x has zeros at - 2, 0, 3 and 7. What are the signs of the values between 0 and 3? Show algebraically how you know.

+3

Answers (1)

Know the Answer?

Andrew · Answer 1

The answer to your question is Positive

Step-by-step explanation:

Function

g (x) = x⁴ - 8x³ + x² + 42x

To know if the function is positive or negative in the interval (0, 3), look for two numbers between this interval and evaluate the function.

The numbers I chose were 1 and 2

- g (1) = (1) ⁴ - 8 (1) ³ + (1) ² + 42 (1)

= 1 - 8 - 1 + 42

= + 36 positive

- g (2) = (2) ⁴ - 8 (2) ³ + (2) ² + 42 (2)

= 16 - 64 + 4 + 84

= + 40

Conclusion

The function is positive in the interval (0, 3)