Question

Find the values of x, which both the inequations x² - 1 ≤ 0 and x² - x - 2 ≥ 0 satisfies.
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Answer 1

$4x { \leqslant 24}^{2} 1224 > 369x = 4$

Answer 2

Solve quadratic inequality: f(x) = x^2 - 3x + 2 > 0

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. Out side 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]}

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