Practice Case 1: No Real Roots (5.1) - Quadratic Inequalities - IB 10 Mathematics – Group 5, Algebra

Practice: Case 1: No Real Roots

Lesson 5.1Quadratic Inequalities

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Find the roots of the equation $x^2 + 4x + 5 = 0$ and determine the nature of the roots.
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Calculate the discriminant to see if it is less than zero.
Question 2.
Does the inequality $x^2 - 3 > 0$ have solutions? If so, where?
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Factor or use the quadratic formula.
3Question 3.
What does a negative discriminant indicate about a quadratic equation?
- It has two real roots.
- It has one real root.
- It has no real roots.
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Remember what the discriminant tells us about intersecting points.
4Question 4.
True or False: A parabola that opens downwards will always result in a true inequality.
- True
- False
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Consider the implications of direction and roots.
Question 5.
Evaluate how the nature of roots impacts the feasibility of solutions in a business model involving fixed costs represented by the quadratic $x^2 + 5x + 6$ . What is the broader implication?
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Check the discriminant first to classify roots.
Question 6.
Discuss the implications of the inequality $-2x^2 + 3x + 5 \geq 0$ when analyzed for real-world applications. What could this represent?
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Graphing may yield insights into solution intervals.

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