Question

Could you solve this inequality, please?

x^4+3x−2≥0
a. x≤−2
b. −2≤x≤−1
c. −1≤x≤1
d. x≥1

Answer 1

To solve the inequality, we can factor the left side and create a sign chart to determine the intervals that satisfy the inequality. The solution is -2≤x≤-1.

Step-by-step explanation:

To solve the inequality, x^4+3x-2≥0, we can factor the left side of the inequality. The factored form is (x-1)(x+2)(x^2+x+1)≥0. To determine the intervals that satisfy the inequality, we can create a sign chart. We know that (x-1)(x+2)≥0 when x≤-2 or −1≤x≤1, and x^2+x+1≥0 for all values of x. Therefore, the solution is b. −2≤x≤−1.