Practice Case 1: No Real Roots - 5.1 | 9. Quadratic Inequalities | IB Class 10 Mathematics – Group 5, Algebra
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5.1 - Case 1: No Real Roots

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Find the roots of the equation \(x^2 + 4x + 5 = 0\) and determine the nature of the roots.

💡 Hint: Calculate the discriminant to see if it is less than zero.

Question 2

Easy

Does the inequality \(x^2 - 3 > 0\) have solutions? If so, where?

💡 Hint: Factor or use the quadratic formula.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

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.

💡 Hint: Remember what the discriminant tells us about intersecting points.

Question 2

True or False: A parabola that opens downwards will always result in a true inequality.

  • True
  • False

💡 Hint: Consider the implications of direction and roots.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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?

💡 Hint: Check the discriminant first to classify roots.

Question 2

Discuss the implications of the inequality \(-2x^2 + 3x + 5 \geq 0\) when analyzed for real-world applications. What could this represent?

💡 Hint: Graphing may yield insights into solution intervals.

Challenge and get performance evaluation