AP POLYCET MATHEMATICS Multiple Choice Questions (MCQs)
AP POLYCET Mathematics - Theory of Equations MCQs (31-45)
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31. What is the number of real roots of the equation \( x^2 + 4x + 5 = 0 \)?
- a) 0
- b) 1
- c) 2
- d) Infinite
Answer: a) 0
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32. Which of the following is the solution for the equation \( x^2 - 5x + 6 = 0 \)?
- a) \( x = 1, 6 \)
- b) \( x = 2, 3 \)
- c) \( x = -1, 6 \)
- d) \( x = -2, 3 \)
Answer: b) \( x = 2, 3 \)
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33. What is the sum of the roots of the quadratic equation \( 2x^2 - 3x - 5 = 0 \)?
- a) -3/2
- b) 3/2
- c) 5/2
- d) -5/2
Answer: b) 3/2
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34. What is the product of the roots of the quadratic equation \( x^2 + 6x + 9 = 0 \)?
- a) 9
- b) 6
- c) 0
- d) -9
Answer: a) 9
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35. For the cubic equation \( x^3 - 6x^2 + 11x - 6 = 0 \), what is the sum of the roots?
- a) 6
- b) -6
- c) 11
- d) -11
Answer: a) 6
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36. Which of the following is the general form of a cubic equation?
- a) \( ax^2 + bx + c = 0 \)
- b) \( ax^3 + bx^2 + cx + d = 0 \)
- c) \( ax + b = 0 \)
- d) \( ax^4 + bx^2 + cx = 0 \)
Answer: b) \( ax^3 + bx^2 + cx + d = 0 \)
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37. If \( x^2 - 5x + 6 = 0 \), then the roots are:
- a) 2 and 3
- b) -2 and -3
- c) 5 and 6
- d) -5 and -6
Answer: a) 2 and 3
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38. What is the value of the discriminant for the quadratic equation \( 4x^2 - 12x + 9 = 0 \)?
- a) 0
- b) 1
- c) 2
- d) 3
Answer: a) 0
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39. Which of the following is a factor of the cubic equation \( x^3 - 7x^2 + 10x - 2 = 0 \)?
- a) \( x - 2 \)
- b) \( x - 1 \)
- c) \( x + 1 \)
- d) \( x - 3 \)
Answer: b) \( x - 1 \)
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40. For the equation \( 2x^3 - 4x^2 + 6x = 0 \), which factor is common?
- a) \( x \)
- b) \( 2x \)
- c) \( 3x \)
- d) \( x^2 \)
Answer: a) \( x \)
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41. If one root of the equation \( x^2 - 3x - 10 = 0 \) is 5, what is the other root?
- a) 2
- b) -2
- c) -5
- d) 10
Answer: b) -2
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42. In the equation \( x^2 + 7x + 10 = 0 \), the product of the roots is:
- a) 10
- b) 7
- c) -10
- d) -7
Answer: c) -10
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43. Which of the following represents a quadratic equation?
- a) \( x^3 + x^2 = 0 \)
- b) \( x^2 + 5x + 6 = 0 \)
- c) \( x^2 + 4 = 0 \)
- d) \( x^4 + 2x = 0 \)
Answer: b) \( x^2 + 5x + 6 = 0 \)
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44. What is the sum of the roots of the quadratic equation \( x^2 + 5x + 6 = 0 \)?
- a) -5
- b) 5
- c) 6
- d) -6
Answer: a) -5
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45. The cubic equation \( x^3 - 3x^2 - 4x + 12 = 0 \) has which root?
- a) 1
- b) -1
- c) 3
- d) -3
Answer: c) 3
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