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Find the zeros of g(x)=4x3+13x2−37x−10 , given its graph. (1 point) Responses x={−10,−5,2} x equals left brace negative 10 comma negative 5 comma 2 right brace x={−10,−5,−14,2} x equals left brace negative 10 comma negative 5 comma negative Start Fraction 1 over 4 End Fraction comma 2 right brace x={−5,−14,2} x equals left brace negative 5 comma negative Start Fraction 1 over 4 End Fraction comma 2 right brace x={−5,2} x equals left brace negative 5 comma 2 right brace

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To find the zeros of the polynomial \( g(x) = 4x^3 + 13x^2 - 37x - 10 \), we can use various methods such as synthetic division or the Rational Root Theorem, but without the graph, we cannot ascertain the exact zeros directly.

If you're provided with a graph, the zeros (or x-intercepts) can be observed visually. Typically, this entails finding the values of \( x \) where the graph intersects the x-axis (i.e., where \( g(x) = 0 \)).

From the options provided:

  1. \( x = {-10, -5, 2} \)
  2. \( x = {-10, -5, -\frac{1}{4}, 2} \)
  3. \( x = {-5, -\frac{1}{4}, 2} \)
  4. \( x = {-5, 2} \)

We can analyze the options based on common polynomial root behavior and the coefficients given. An initial rough estimate or a graph (which were not provided here) could suggest the potential roots.

Without the graph or further context, we assume we need to evaluate the responses directly.

If the graph shows intersections at \( x = -10, -5, \) and \( 2 \), then the correct response would be:

Answer: \( x = {-10, -5, 2} \)