Solve the following inequality

Question

(2x+1)(x^2-x+2)≤0

In terms of x.

Please help and explain in detail the step-by-step process my homework is very confusing 🙏

Answer 1

the inequality/equality is true when both factors are either

opposite sign

or

either one = 0

find the x values that make that happen

such as setting each factor = 0 and solving for x

that's half the solution

x=-1/2 and x= 1/2 +/-.5sqr(1-4(2))= .5+/-.5isqr7

one real and two imaginary solutions, to make the equality true

use the quadratic formula to find the two imaginary solutions

then solve for the inequality

such that x makes the two factors of opposite sign

first guess is x<-1/2 which makes 1st factor negative and 2nd factor positive

graph the cubic and check the answer, x<-1/2 is when y<0

x=-1/2 is when y=0

plus the two imaginary solutions you can't see on the graph