Class 10 Mathematics: Advanced Quadratic Equations

This worksheet challenges students to solve complex problems involving quadratic equations, roots, and their properties. It covers a range of question types to test conceptual understanding and problem-solving skills.

Class 10CBSEMathematicshardPractice

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Preview · 10 questions

Q1. If the roots of the quadratic equation (b - c)x² + (c - a)x + (a - b) = 0 are equal, then which of the following is true?
- a + c = 2b
- b + c = 2a
- a + b = 2c
- a + b + c = 0
Q2. For what value of k, the roots of the quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 are real and equal?
- k = 1 or k = 3
- k = 1 or k = -3
- k = -1 or k = 3
- k = -1 or k = -3
Q3. If one root of the equation x² + px + q = 0 is the square of the other, then which of the following relations is correct?
- p³ - q(3p - 1) + q² = 0
- p³ + q(3p + 1) + q² = 0
- p³ + q(3p - 1) + q² = 0
- p³ - q(3p + 1) + q² = 0
Q4. If sinθ and cosθ are the roots of the equation ax² + bx + c = 0, then which among the following is true?
- a² - b² + 2ac = 0
- a² + b² + 2ac = 0
- a² - b² - 2ac = 0
- a² + b² - 2ac = 0
Q5. A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, then the number of days B alone would take to finish the work is:
- 10 days
- 12 days
- 14 days
- 16 days

+ 5 more in the printable PDF.