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15 Quadratic problems Questions and Answers

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

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Practice quadratic problems questions with detailed explanations. These solved examples cover the most frequently asked patterns in placement and competitive exams.

Q1 Easy

Find roots of x^2 + 12x + 36 = 0

  • A. -6, -6 ✓
  • B. -6, 6
  • C. 6, -6
  • D. 6, 6
Explanation: x^2 + 12x + 36 = (x+6)(x+6). Roots are -6 and -6.
Q2 Easy

Find roots of x^2 + 14x + 48 = 0

  • A. 8, 6
  • B. -8, -6 ✓
  • C. -8, 6
  • D. 8, -6
Explanation: x^2 + 14x + 48 = (x+8)(x+6). Roots are -8 and -6.
Q3 Easy

Find roots of x^2 + 9x + 14 = 0

  • A. 2, 7
  • B. 2, -7
  • C. -2, 7
  • D. -2, -7 ✓
Explanation: x^2 + 9x + 14 = (x+2)(x+7). Roots are -2 and -7.
Q4 Easy

For x^2 - 13x + 30 = 0, what is the product of roots?

  • A. 33
  • B. 24
  • C. 27
  • D. 30 ✓
Explanation: Product of roots = c/a = 30/1 = 30.
Q5 Easy

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

  • A. 51
  • B. 57
  • C. 48
  • D. 54 ✓
Explanation: Product of roots = c/a = 54/1 = 54.
Q6 Easy

Find roots of x^2 + 15x + 54 = 0

  • A. 9, 6
  • B. -9, 6
  • C. 9, -6
  • D. -9, -6 ✓
Explanation: x^2 + 15x + 54 = (x+9)(x+6). Roots are -9 and -6.
Q7 Medium

For x^2 - 11x + 10 = 0, what is the product of roots?

  • A. 13
  • B. 10 ✓
  • C. 7
  • D. 4
Explanation: Product of roots = c/a = 10/1 = 10.
Q8 Medium

For x^2 - 18x + 80 = 0, what is the product of roots?

  • A. 83
  • B. 80 ✓
  • C. 77
  • D. 74
Explanation: Product of roots = c/a = 80/1 = 80.
Q9 Medium

For x^2 - 11x + 24 = 0, what is the sum of roots?

  • A. 11 ✓
  • B. 13
  • C. 9
  • D. 8
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 11.
Q10 Medium

For x^2 - 14x + 45 = 0, what is the sum of roots?

  • A. 11
  • B. 12
  • C. 14 ✓
  • D. 16
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 14.
Q11 Medium

Find roots of x^2 + 7x + 12 = 0

  • A. 4, 3
  • B. -4, 3
  • C. -4, -3 ✓
  • D. 4, -3
Explanation: x^2 + 7x + 12 = (x+4)(x+3). Roots are -4 and -3.
Q12 Hard

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

  • A. 21
  • B. 12
  • C. 18 ✓
  • D. 15
Explanation: Product of roots = c/a = 18/1 = 18.
Q13 Hard

For x^2 - 13x + 22 = 0, what is the sum of roots?

  • A. 13 ✓
  • B. 11
  • C. 10
  • D. 15
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 13.
Q14 Hard

For x^2 - 19x + 88 = 0, what is the sum of roots?

  • A. 21
  • B. 17
  • C. 16
  • D. 19 ✓
Explanation: For ax^2+bx+c=0, sum = -b/a. Here sum = 19.
Q15 Hard

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

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

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