Grade 12 Math: Discriminant Worksheet
This worksheet focuses on understanding and applying the discriminant to analyze the nature of roots of quadratic equations.
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Grade 12 Math: Discriminant Analysis
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula Δ = .
2. If the discriminant is positive (Δ > 0), the quadratic equation has real roots.
3. If the discriminant is zero (Δ = 0), the quadratic equation has real root.
4. If the discriminant is negative (Δ < 0), the quadratic equation has real roots.
5. What is the discriminant of the quadratic equation 3x² - 5x + 2 = 0?
1
-1
49
-49
6. For which equation is the discriminant equal to 0?
x² + 4x + 3 = 0
x² - 6x + 9 = 0
2x² + x + 1 = 0
x² + 2x - 3 = 0
7. Determine the nature of the roots for the quadratic equation 2x² + 7x + 3 = 0. Justify your answer using the discriminant.
8. Consider the equation x² - 10x + 25 = 0. Calculate the discriminant and describe the nature of its roots.
Match each discriminant value with the corresponding nature of roots.
9. Δ = 16
a. One real root (repeated)
10. Δ = -9
b. Two distinct real roots
11. Δ = 0
c. Two complex conjugate roots
12. Find the value(s) of 'k' for which the quadratic equation x² + kx + 9 = 0 has exactly one real root.
13. For what values of 'm' does the equation mx² - 4x + 1 = 0 have two distinct real roots?