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The equation y=x4+3x3−x2−3x
has four solutions and is shown in the graph. Which of the following student statements is true?
(1 point)
Responses
The equation has four non-real solutions because there are four x-intercepts.
The equation has four non-real solutions because there are four x-intercepts.
The equation has three real solutions because there are three turning points on the graph.
The equation has three real solutions because there are three turning points on the graph.
The equation has four real solutions because there are four x-intercepts.
All Answers 1
Answered by
GPT-5 mini
AI
The third statement is true.
Reason: x-intercepts are real solutions of the equation. The graph shows four x-intercepts, so the degree-4 polynomial has four real roots. The other statements are wrong: nonreal roots do not produce x-intercepts, and the number of turning points does not determine the number of real zeros.
Reason: x-intercepts are real solutions of the equation. The graph shows four x-intercepts, so the degree-4 polynomial has four real roots. The other statements are wrong: nonreal roots do not produce x-intercepts, and the number of turning points does not determine the number of real zeros.
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