Quadratic Equations – Nature of Roots, Symmetric Functions of Roots

Grade 11 Maths Higher — Quadratic Equations – Nature of Roots, Symmetric Functions of Roots: 25 practice questions with instant scoring and explanations.

1. For ax² + bx + c = 0, if Δ = b² - 4ac > 0 and a rational, the roots are:
2. The nature of roots of x² + 4x + 4 = 0 is:
3. For what value of k will x² + 2kx + 9 = 0 have equal roots?
4. If α and β are roots of x² + px + q = 0, then α² + β² =
5. For roots α and β of ax² + bx + c = 0, the sum α + β equals:
6. For roots α and β, the product αβ equals:
7. If α and β are roots of x² - 5x + 6 = 0, then 1/α + 1/β =
8. For the quadratic 2x² + 3x - 2 = 0, find α² + β²:
9. If roots of x² + px + q = 0 are in ratio 2:3, then 9p² =
10. For roots α and β, the sum α³ + β³ =
11. The condition for roots of x² + px + q = 0 to be equal is:
12. If the roots are reciprocals, and their sum is 2.5, the quadratic is:
13. If one root is the square of the other and their sum is 12, the roots are:
14. For x² + 6x + k = 0 to have roots with absolute difference 4, k equals:
15. If α and β are roots of x² - px + q = 0, then (α - β)² =
16. The quadratic with roots α + β and αβ (where α, β are roots of x² - 5x + 6 = 0) is:
17. For what value of m are the roots of x² - mx + 1 = 0 equal?
18. If α³ + β³ = 35 and α + β = 5, then αβ =
19. For roots that are opposite in sign with product -6, the quadratic is:
20. If α/β + β/α = 8/3 and α + β = 4, then αβ =
21. The condition for x² + 2px + 2q = 0 to have roots in 1:2 ratio is:
22. For biquadratic x⁴ + px² + q = 0, if roots are α, -α, β, -β, then p + q in terms of a root α is:
23. If the roots of 3x² + 6x + p = 0 differ by 2, then p =
24. For the equation x² - px + q = 0, the sum of roots raised to power 4 is:
25. If the roots of x² + 5x + k = 0 are in the ratio 1:2, then k =