Practice Example 2: Solve 2𝑥² − 8𝑥 + 6 ≥ 0 (3.2)

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6 sample questions

Question 1.
Solve x² + 2x - 15 > 0.
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Find the roots by factoring or using the quadratic formula.
Question 2.
Solve x² - 4x + 4 ≤ 0.
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This one is a perfect square.
3Question 3.
What form must a quadratic inequality be in to solve it?
- ax² + bx + c = 0
- ax² + bx + c < 0
- ax² + bx + c ≥ 0
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Remember the structure of quadratic inequalities.
4Question 4.
True or False: The roots of the quadratic equation do not play a role in analyzing a quadratic inequality.
- True
- False
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Consider how we determine where solutions lie.
Question 5.
Consider the inequality 2𝑥² − 4𝑥 + 2 < 0. Analyze the solutions and discuss the implications if the discriminant is zero.
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Use the discriminant to determine the nature of the roots.
Question 6.
A company's profit, expressed as a quadratic function, is modeled by P(x) = -2x² + 12x - 10. Determine the production levels where the profit is greater than zero.
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Remember to find the roots first, then analyze the interval between them.

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