Use the x-intercept method to find the solution of the equation below where . Round your answer to five decimal places.
A) x = 0.71845
B) x = -2.55178
C) x = 3.46845
D) x = -1.91319
E) x = -0.07986

Question

Use the x-intercept method to find the solution of the equation below where  . Round your answer to five decimal places. ​  ​
A) x = 0.71845 
B) x = -2.55178 
C) x = 3.46845 
D) x = -1.91319 
E) x = -0.07986

Quizplus · Accepted Answer

To use the x-intercept method, we set y=0 in the equation and solve for x.

2x^3 + 11x^2 + 9x - 10 = 0

If we set x = 0, we get:

-10 = 0

This is not true, so x = 0 is not an x-intercept.

Next, we factor the equation as much as possible:

2x^3 + 11x^2 + 9x - 10 = (2x-1)(x+5)(x+1)

Setting each factor equal to 0 gives us the x-intercepts:

2x-1 = 0 -> x = 0.5 
x+5 = 0 -> x = -5 
x+1 = 0 -> x = -1

Therefore, the solutions are x = 0.5, x = -5, and x = -1. 
Of these options, only A rounds to a five-decimal place answer.

Use the X-Intercept Method to Find the Solution of the Equation