SAT Exam > SAT Questions > x3(x2− 5) = − 4xIf x > 0, what...
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x3(x2 − 5) = − 4x
If x > 0, what is one possible solution to the equation above?
If x > 0, what is one possible solution to the equation above?
- a)1
- b)2
- c)both of the above
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
x3(x2− 5) = − 4xIf x > 0, what is one possible solution...
The correct answer is either 1 or 2. The given equation can be rewritten as x5 − 5x3 + 4x = 0. Since the polynomial expression on the left has no constant term, it has x as a factor: x(x4 − 5x2 + 4) = 0. The expression in parentheses is a quadratic equation in x2 that can be factored, giving x(x2 − 1)(x2 − 4) = 0. This further factors as x(x − 1)(x + 1)(x − 2)(x + 2) = 0. The solutions for x are x = 0, x = 1, x = −1, x = 2, and x = −2. Since it is given that x > 0, the possible values of x are x = 1 and x = 2. Either 1 or 2 may be gridded as the correct answer.
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x3(x2− 5) = − 4xIf x > 0, what is one possible solution to the equation above?a)1b)2c)both of the aboved)None of theseCorrect answer is option 'C'. Can you explain this answer?
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