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30 Quadratic problems Questions and Answers

30 solved Quadratic problems questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced quadratic problems questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

ax² + bx + c = 0 Roots: x = [-b ± sqrt(b²-4ac)] / 2a Sum of roots = -b/a, Product of roots = c/a Discriminant: D = b² - 4ac (D>0 real, D=0 equal, D<0 complex)
Q1 Medium

For x^2 - 10x + 25 = 0, what is the sum of roots?

  • A. 7
  • B. 8
  • C. 10 ✓
  • D. 12
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 10.
Q2 Medium

For x^2 - 18x + 77 = 0, what is the sum of roots?

  • A. 18 ✓
  • B. 16
  • C. 20
  • D. 15
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 18.
Q3 Medium

For x^2 - 10x + 21 = 0, what is the product of roots?

  • A. 21 ✓
  • B. 15
  • C. 18
  • D. 24
Explanation: Product of roots = c/a = 21/1 = 21.
Q4 Medium

For x^2 - 11x + 18 = 0, what is the sum of roots?

  • A. 13
  • B. 9
  • C. 11 ✓
  • D. 8
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 11.
Q5 Medium

For x^2 - 20x + 100 = 0, what is the product of roots?

  • A. 100 ✓
  • B. 94
  • C. 103
  • D. 97
Explanation: Product of roots = c/a = 100/1 = 100.
Q6 Medium

For x^2 - 6x + 5 = 0, what is the product of roots?

  • A. 5 ✓
  • B. 8
  • C. 11
  • D. 2
Explanation: Product of roots = c/a = 5/1 = 5.
Q7 Medium

For x^2 - 19x + 90 = 0, what is the product of roots?

  • A. 90 ✓
  • B. 93
  • C. 87
  • D. 84
Explanation: Product of roots = c/a = 90/1 = 90.
Q8 Medium

For x^2 - 10x + 16 = 0, what is the product of roots?

  • A. 16 ✓
  • B. 10
  • C. 13
  • D. 19
Explanation: Product of roots = c/a = 16/1 = 16.
Q9 Medium

For x^2 - 14x + 48 = 0, what is the product of roots?

  • A. 42
  • B. 45
  • C. 51
  • D. 48 ✓
Explanation: Product of roots = c/a = 48/1 = 48.
Q10 Medium

For x^2 - 9x + 18 = 0, what is the sum of roots?

  • A. 6
  • B. 9 ✓
  • C. 11
  • D. 7
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 9.
Q11 Medium

For x^2 - 8x + 7 = 0, what is the product of roots?

  • A. 10
  • B. 7 ✓
  • C. 1
  • D. 4
Explanation: Product of roots = c/a = 7/1 = 7.
Q12 Medium

For x^2 - 5x + 4 = 0, what is the product of roots?

  • A. 1
  • B. 4 ✓
  • C. 7
  • D. 10
Explanation: Product of roots = c/a = 4/1 = 4.
Q13 Medium

Find roots of x^2 + 11x + 30 = 0

  • A. 6, -5
  • B. -6, 5
  • C. -6, -5 ✓
  • D. 6, 5
Explanation: x^2 + 11x + 30 = (x+6)(x+5). Roots are -6 and -5.
Q14 Medium

For x^2 - 9x + 20 = 0, what is the sum of roots?

  • A. 6
  • B. 9 ✓
  • C. 11
  • D. 7
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 9.
Q15 Medium

For x^2 - 15x + 54 = 0, what is the sum of roots?

  • A. 17
  • B. 12
  • C. 15 ✓
  • D. 13
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 15.
Q16 Medium

For x^2 - 16x + 48 = 0, what is the sum of roots?

  • A. 16 ✓
  • B. 14
  • C. 13
  • D. 18
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 16.
Q17 Medium

For x^2 - 18x + 72 = 0, what is the sum of roots?

  • A. 18 ✓
  • B. 15
  • C. 16
  • D. 20
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 18.
Q18 Medium

Find roots of x^2 + 8x + 16 = 0

  • A. -4, 4
  • B. 4, -4
  • C. -4, -4 ✓
  • D. 4, 4
Explanation: x^2 + 8x + 16 = (x+4)(x+4). Roots are -4 and -4.
Q19 Medium

For x^2 - 9x + 8 = 0, what is the product of roots?

  • A. 11
  • B. 8 ✓
  • C. 5
  • D. 2
Explanation: Product of roots = c/a = 8/1 = 8.
Q20 Medium

For x^2 - 17x + 70 = 0, what is the product of roots?

  • A. 73
  • B. 70 ✓
  • C. 67
  • D. 64
Explanation: Product of roots = c/a = 70/1 = 70.
Q21 Medium

For x^2 - 12x + 35 = 0, what is the product of roots?

  • A. 29
  • B. 38
  • C. 32
  • D. 35 ✓
Explanation: Product of roots = c/a = 35/1 = 35.
Q22 Medium

For x^2 - 12x + 27 = 0, what is the sum of roots?

  • A. 12 ✓
  • B. 10
  • C. 14
  • D. 9
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 12.
Q23 Medium

For x^2 - 4x + 4 = 0, what is the sum of roots?

  • A. 2
  • B. 1
  • C. 6
  • D. 4 ✓
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 4.
Q24 Medium

For x^2 - 7x + 10 = 0, what is the sum of roots?

  • A. 9
  • B. 7 ✓
  • C. 5
  • D. 4
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 7.
Q25 Medium

For x^2 - 16x + 60 = 0, what is the sum of roots?

  • A. 18
  • B. 14
  • C. 13
  • D. 16 ✓
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 16.
Q26 Medium

For x^2 - 13x + 36 = 0, what is the sum of roots?

  • A. 15
  • B. 11
  • C. 13 ✓
  • D. 10
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 13.
Q27 Medium

For x^2 - 16x + 60 = 0, what is the product of roots?

  • A. 60 ✓
  • B. 54
  • C. 63
  • D. 57
Explanation: Product of roots = c/a = 60/1 = 60.
Q28 Medium

For x^2 - 12x + 20 = 0, what is the sum of roots?

  • A. 10
  • B. 12 ✓
  • C. 14
  • D. 9
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 12.
Q29 Medium

For x^2 - 17x + 72 = 0, what is the product of roots?

  • A. 72 ✓
  • B. 66
  • C. 75
  • D. 69
Explanation: Product of roots = c/a = 72/1 = 72.
Q30 Medium

For x^2 - 20x + 100 = 0, what is the sum of roots?

  • A. 20 ✓
  • B. 18
  • C. 22
  • D. 17
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 20.

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