Grade 10 Discriminant Worksheet
This worksheet focuses on understanding and applying the discriminant to determine the nature of roots of quadratic equations for Grade 10 students.
Includes
Standards
Discriminant Practice
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula Δ = b² - 4ac. It helps determine the nature of the roots of the quadratic equation.
• If Δ > 0, there are two distinct real roots.
• If Δ = 0, there is exactly one real root (a repeated root).
• If Δ < 0, there are two complex conjugate roots (no real roots).
1. What is the value of the discriminant for the quadratic equation 2x² - 5x + 3 = 0?
1
-1
49
-49
2. If the discriminant of a quadratic equation is 0, what can be said about its roots?
Two distinct real roots
One real root (repeated)
Two complex conjugate roots
No roots
3. If the discriminant is a positive number, the quadratic equation has real roots.
4. When the discriminant is negative, the quadratic equation has roots.
5. Determine the nature of the roots for the equation x² + 6x + 9 = 0. Show your work.
6. Find the value(s) of 'k' for which the quadratic equation kx² + 4x + 1 = 0 has exactly one real root. Show your work.
7. A negative discriminant means the parabola intersects the x-axis at two distinct points.
True
False
8. If the discriminant is a perfect square and positive, the quadratic equation has rational roots.
True
False
9. A projectile's height h (in meters) at time t (in seconds) is given by h(t) = -5t² + 20t + 15. Will the projectile ever reach a height of 40 meters? Use the discriminant to justify your answer.