Question

Given the following factors, find all the roots of the equation (4x−3)(x^2+2)=0. Which of the following options correctly lists all the roots?

A) x = 3/4, x = √2, x = -√2
B) x = 3/4, x = -√2
C) x = 3/4, x = √2
D) x = 3/4, x = -√2, x = √2

Answer 1

To find the roots of the equation (4x−3)(x²+2)=0, set each factor equal to zero and solve for x. The only root of the equation is x = 3/4.

Step-by-step explanation:

To find the roots of the equation (4x−3)(x²+2)=0, we can set each factor equal to zero and solve for x.

First, setting 4x - 3 = 0, we add 3 to both sides and divide by 4 to get x = 3/4.

Next, setting x² + 2 = 0, we subtract 2 from both sides, take the square root of both sides, and solve for x. However, there is no real number solution to this equation, so it has no real roots.

Therefore, the only root of the equation (4x−3)(x²+2)=0 is x = 3/4.