Question

The solution set of x² + 2 ≤ 3x ≤ 2x² - 5, is
(a) ⏀ (b) [1, 2] (c) (- [infinity], - 1) U [5/2, [infinity]) (d) none of these

Answer 1

Ans:

(-infinity, 1) and (2, +infinity)

Explanation :

First solve f(x) = x^2 - 3x + 2 = 0

Since (a + b + c = 0), use the Shortcut. The 2 real roots are x = 1 and x = c/a = 2.

Use the algebraic method to solve f(x) > 0. Since a > 0, the parabola opens upward. Inside the interval (1, 2), f(x) is negative. Outside the interval (1, 2), f(x) is positive.

Answer by open intervals: (-infinity, 1) and (2, +infinity)

graph{x^2 - 3x + 2 [-10, 10, -5, 5]}