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How do I find the solutions to 8x^3-x+7

1 Answer

3 votes

Answer:

x = -1

Explanation:

You can use rational root test to check for rational roots.

Factors of 8: 1, 2, 4, 8

Factors of 7: 1, 7

Possible rational roots: ±1/1, ±1/2, ±1/4, ±1/8, ±7/1, ±7/2, ±7/4, ±7/8

Checking, we find that -1 is a root. Knowing that, we can use grouping to factor:

8x³ − x + 7

8x³ + 8x² − 8x² − x + 7

8x² (x + 1) − (8x² + x − 7)

8x² (x + 1) − (8x − 7) (x + 1)

(8x² − (8x − 7)) (x + 1)

(8x² − 8x + 7) (x + 1)

Using the quadratic formula, we find that 8x² − 8x + 7 has no real solutions.

Therefore, the only solution is x = -1.

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