Practice Nature Of Roots Using Discriminant (3) - Quadratic Equations - IB 10 Mathematics

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6 sample questions

Question 1.
Calculate the discriminant for the equation x² + x + 1 = 0.
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Remember to use the formula D = b² - 4ac.
Question 2.
What is the nature of the roots for the equation 2x² - 4x + 2 = 0?
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Calculate the discriminant using the provided coefficients.
3Question 3.
What happens if the discriminant D is greater than 0?
- Two distinct real roots
- No real roots
- Two equal real roots
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Think about the nature of different root situations in relation to the graph.
4Question 4.
True or False: If D = 0, the equation has complex roots.
- True
- False
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Consider what it means for points to be equal on the graph.
Question 5.
For a quadratic equation represented by ax² + (k-1)x + (k-3) = 0, where k is a parameter, determine the value(s) of k that lead to complex roots.
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Start by calculating the discriminant.
Question 6.
Prove that the roots are real if and only if the quadratic is represented by the inequality a(b² - 4ac) > 0.
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Analyze the definitions of each scenario and ensure you refer back to the discriminant.

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