Example 1 · level 1
What is the nature of the roots of 4x² + x + 4 = 0?
- Two distinct real roots
- Cannot be decided
- No real roots
- Two equal real roots
Show solution
- D = 1 − 64 = −63.
- D < 0, so: no real roots.
Answer: No real roots
CLASS 10 MATHS · QUADRATIC EQUATIONS
Nature of roots and the discriminant
For ax² + bx + c = 0, D = b² − 4ac. D > 0: two distinct real roots; D = 0: two equal roots; D < 0: no real roots.
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Worked examples
Example 2 · level 2
Find the positive value of k for which 16x² + kx + 9 = 0 has two equal roots.
Show solution
- D = k² − 4 × 16 × 9 = 0
- k² = 576
- k = 24 (taking the positive value).
Answer: 24
Example 3 · level 3
Find the positive value of k for which 48x² + kx + 27 = 0 has two equal roots.
Show solution
- D = k² − 4 × 48 × 27 = 0
- k² = 5184
- k = 72 (taking the positive value).
Answer: 72