Ask Question
8 September, 18:22

Which statement describes the graph of f (x) = - x4 + 3x3 + 10x2?

The graph crosses the x axis at x = 0 and touches the x axis at x = 5 and x = - 2.

The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = - 2.

The graph crosses the x axis at x = 0 and touches the x axis at x = - 5 and x = 2.

The graph touches the x axis at x = 0 and crosses the x axis at x = - 5 and x = 2.

+3
Answers (1)
  1. 8 September, 20:14
    0
    f (x) = - x^4 + 3x^3 + 10x^2 = - x^2 (x^2 - 3x - 10) = - x^2 (x^2 + 2x - 5x - 10) = - x^2[x (x + 2) - 5 (x + 2) ] = - x^2 (x - 5) (x + 2) Thus f (x) = - x^4 + 3x^3 + 10x^2 has roots of 0 with multiplicity of 2, 5 with multiplicity of 1 and - 2 with multiplicity of 1. Therefore, the graph of f (x) = - x^4 + 3x^3 + 10x^2 touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = - 2. The correct answer to the question "Which statement describes the graph of f (x) = - x^4 + 3x^3 + 10x^2?" is "The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = - 2."
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Which statement describes the graph of f (x) = - x4 + 3x3 + 10x2? The graph crosses the x axis at x = 0 and touches the x axis at x = 5 and ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers