Find the zeros of g(x)=4x^3+13x^2−37x−10 , given its graph.
a. x= {-10, -5, 2}
b. x= {-10,-5, - 1/4, 2}
c. x= {-5,2}
d. x= {-5, - 1/4, 2}
To find the zeros of a function, we need to find the values of x where the function equals zero. Looking at the given graph, we can see that the function crosses the x-axis at x = -10, x = -5, and x = 2. Therefore, the correct answer is:
a. x = {-10, -5, 2}
To find the zeros of the function g(x) = 4x^3 + 13x^2 - 37x - 10, we need to find the x-values where the graph of the function intersects the x-axis.
Based on the given options (a, b, c, d), we can determine the correct answer by substituting each option into the equation g(x) = 0 and checking if it satisfies the equation.
a. x = {-10, -5, 2}
Substituting these values into the equation:
For x = -10: g(-10) = 4(-10)^3 + 13(-10)^2 - 37(-10) - 10 = -2840
For x = -5: g(-5) = 4(-5)^3 + 13(-5)^2 - 37(-5) - 10 = 0
For x = 2: g(2) = 4(2)^3 + 13(2)^2 - 37(2) - 10 = 0
Since g(-5) = 0 and g(2) = 0, option a (x = {-10, -5, 2}) satisfies the equation and is a potential solution.
b. x = {-10, -5, -1/4, 2}
Substituting these values into the equation:
For x = -10: g(-10) = -2840 (not equal to 0)
For x = -5: g(-5) = 0
For x = -1/4: g(-1/4) = 0
For x = 2: g(2) = 0
Since g(-5) = 0, g(-1/4) = 0, and g(2) = 0, option b (x = {-10, -5, -1/4, 2}) satisfies the equation and is a potential solution.
c. x = {-5, 2}
Substituting these values into the equation:
For x = -5: g(-5) = 0
For x = 2: g(2) = 0
Since g(-5) = 0 and g(2) = 0, option c (x = {-5, 2}) satisfies the equation and is a potential solution.
d. x = {-5, -1/4, 2}
Substituting these values into the equation:
For x = -5: g(-5) = 0
For x = -1/4: g(-1/4) = 0
For x = 2: g(2) = 0
Since g(-5) = 0, g(-1/4) = 0, and g(2) = 0, option d (x = {-5, -1/4, 2}) satisfies the equation and is a potential solution.
Therefore, the correct answer is option d: x = {-5, -1/4, 2}.
To find the zeros of a function, we need to find the values of x for which the function equals zero. In other words, we need to solve the equation g(x) = 0.
Given the function g(x) = 4x^3 + 13x^2 - 37x - 10, we can find the zeros by factoring the polynomial or by using numerical methods.
However, since we are given the graph of the function, we can determine the zeros by looking at where the graph intersects the x-axis. The x-intercepts are the points on the graph where y = 0.
Looking at the graph, we can see that the graph intersects the x-axis at three points. These points correspond to the zeros of the function. By analyzing the graph or using a calculator, we can find the approximate values of the zeros.
After examining the graph, it appears that the three zeros are at x = -10, x = -5, and x = 2. Therefore, the answer is:
a. x = {-10, -5, 2}