1. Solve the quadratic equation x² - 5x + 6 = 0 by factorisation.
- Ax = 2, x = 3
- Bx = -2, x = -3
- Cx = 1, x = 6
- Dx = -1, x = -6
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Answer: A) x = 2, x = 3
Factor the equation as (x - 2)(x - 3) = 0. The solutions are x = 2 and x = 3.
Class 10 Quadratic Equations — practice questions with answers
Quadratic Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. What is the sum of the roots of the equation 2x² - 3x + 1 = 0?
- A1.5
- B-1.5
- C0.5
- D3
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Answer: A) 1.5
The sum of the roots is given by .
3. Determine the nature of the roots of 2x² - 6x + 3 = 0.
- ATwo distinct real roots
- BTwo equal real roots
- CNo real roots
- DExactly three roots
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Answer: A) Two distinct real roots
Discriminant = (-6)² - 4(2)(3) = 36 - 24 = 12 > 0, so the roots are real and distinct.
4. The length of a rectangular plot is 3 metres more than its breadth, and its area is 70 square metres. What is the breadth (in metres)?
- A8
- B14
- C7
- D6
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Answer: C) 7
Let breadth = x, length = x + 3. Then x(x + 3) = 70, i.e. x² + 3x - 70 = 0, so (x + 10)(x - 7) = 0. The positive value is x = 7 m.
5. The sum of the squares of two consecutive odd positive integers is 290. Find the smaller integer.
- A22
- B10
- C11
- D12
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Answer: C) 11
Let the integers be x and x+2. Then x² + (x+2)² = 290, i.e. 2x² + 4x + 4 = 290, so x² + 2x - 143 = 0, giving (x + 13)(x - 11) = 0. The positive value is x = 11.
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