9
QuizMultiple Choice

Polynomial Inequalities

Question 9 • FL-1200330-Algebra 2 CR

What is the solution to x 4 – 12x 2 + 10 > 0?

Answer
A
(–0.95, 0.95)
B
(–3.33, 3.33)
C
(–3.33, –0.95) U (0.95, 3.33)
D
(–ꝏ, –3.33) U (–0.95, 0.95) U (3.33, ꝏ)

Explanation

Let y = x², so the inequality becomes y² − 12y + 10 > 0. The equation y² − 12y + 10 = 0 has roots y = 6 ± √26, approximately 0.90 and 11.10; taking square roots gives x-values of about ±0.95 and ±3.33. Since the quartic opens upward, it is positive outside its four roots, giving (−∞, −3.33) ∪ (−0.95, 0.95) ∪ (3.33, ∞), choice D.

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