Find the set of real solutions of this inequation:
2x² − 6x + 5 > 0
A) (1, 2)
B) (−∞, 1) ∪ (2, +∞)
C) ∅
D) {1, 2}
E) ℝ
IMAT 2023 · Question 49
Q49 - Algebraic inequalities
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The correct answer is E) ℝ.
Check the discriminant: 36 − 40 = −4. It's negative, so the parabola never touches the x-axis, and since the x² coefficient is positive it sits entirely above it.
The inequality is true for every real x.
The options with 1 and 2 are the roots of 2x² − 6x + 4, which is a different expression.
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