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Theory of quadratic equations

Class 10 · Mathematics · 9 questions

Name: ____________________   Date: ____________

  1. The discriminant of ax² + bx + c = 0 is:

    • A -b / 2a
    • B 4ac
    • C b² + 4ac
    • D b² - 4ac
  2. If the discriminant is negative, the roots are:

    • A Complex
    • B Real and distinct
    • C Rational
    • D Real and equal
  3. The sum of the roots of x² - 7x + 12 = 0 is:

    • A -7
    • B -12
    • C 7
    • D 12
  4. The product of the roots of x² - 7x + 12 = 0 is:

    • A -12
    • B 7
    • C -7
    • D 12
  5. The discriminant of x² - 4x + 4 = 0 is:

    • A 4
    • B 16
    • C -4
    • D 0
  6. The roots of x² + 1 = 0 are:

    • A Real and equal
    • B Complex
    • C Real and distinct
    • D Rational
  7. If the discriminant is a positive perfect square, the roots are:

    • A Rational and unequal
    • B Complex
    • C Irrational
    • D Equal
  8. For x² - 6x + 8 = 0 the sum of the roots is:

    • A -6
    • B 6
    • C 8
    • D -8
  9. The discriminant of x² + 5x + 6 = 0 is:

    • A 49
    • B 1
    • C 25
    • D -1

Answer key

1. D, 2. A, 3. C, 4. D, 5. D, 6. B, 7. A, 8. B, 9. B

  1. Discriminant = b² - 4ac.

  2. A negative discriminant gives complex roots.

  3. Sum = -b / a = 7.

  4. Product = c / a = 12.

  5. 16 - 16 = 0, so the roots are real and equal.

  6. The discriminant is -4, which is negative.

  7. They can be written as fractions.

  8. Sum = -b / a = 6.

  9. 25 - 24 = 1.