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Quadratic Equations

Solving quadratic equations, finding roots, and analyzing their nature

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Questions

Question 1 Multiple Choice (Single Answer)

Solve x2 - 5x + 6.

  1. x = 2, 3
  2. x = - 2, - 3
  3. x = 0, 6
  4. Irrational roots
  5. None of these
Question 2 Multiple Choice (Single Answer)

The roots of x2 - 3x + 16 = 0 are

  1. equal
  2. rational
  3. irrational
  4. imaginary
  5. None of these
Question 3 Multiple Choice (Single Answer)

ax2 + bx + c is a/an

  1. quadratic equation
  2. linear expression
  3. quadratic expression
  4. cubic expression
  5. None of these
Question 4 Multiple Choice (Single Answer)

The solutions of 3x2 - 4x + 1 = 0 are

  1. 0, 0
  2. 1, 2
  3. 3, 1/3
  4. 1, 1/3
  5. None of these
Question 5 Multiple Choice (Single Answer)

If a, b are roots of 2x2 - 7x - 3 = 0, then ab is equal to

  1. 7/2
  2. 3/2
  3. - 3/2
  4. - 3
  5. None of these
Question 6 Multiple Choice (Single Answer)

The sum of roots of x2 - 3x + 2 = 0 is

  1. 1
  2. 3
  3. - 3/2
  4. - 3
  5. None of these
Question 7 Multiple Choice (Single Answer)

The equation 16x2 - 8x + 1 = 0 has

  1. equal roots
  2. imaginary roots
  3. irrational roots
  4. rational, but distinct roots
  5. None of these
Question 8 Multiple Choice (Single Answer)

The nature of the roots of 2x2 - 6x - 3 = 0 is

  1. irrational
  2. real and equal
  3. real, rational and distinct
  4. imaginary
  5. None of these
Question 9 Multiple Choice (Single Answer)

If the roots of equation 10x2 - 2x - m = 0 are equal, then

  1. m = 2
  2. m = - 1/10
  3. m = 3
  4. m = 0
  5. None of these
Question 10 Multiple Choice (Single Answer)

Find the quadratic equation with real coefficients which has one root as 1 + 2i.

  1. x2 - 2x - 5 = 0
  2. x2 - 2x + 5 = 0
  3. x2 + 2x + 5 = 0
  4. x2 + 2x - 5 = 0
  5. None of these
Question 11 Multiple Choice (Single Answer)

Solve 7x2 - 9x + 2 = 0.

  1. x = 1, 2/7
  2. x = 1/7, 2
  3. x = - 1, 2/7
  4. x = 1, - 2/7
  5. None of these
Question 12 Multiple Choice (Single Answer)

If the equation x2 - 9x + m = 0 has only imaginary roots, find the value of m.

  1. m = 20
  2. m = 20 or 25
  3. m < 20 or 25
  4. m > 20.25
  5. None of these
Question 13 Multiple Choice (Single Answer)

If m, n are roots of x2 - 3x + 4 = 0, find the value of (m - n)2.

  1. - 7
  2. 5
  3. 2
  4. 3
  5. None of these
Question 14 Multiple Choice (Single Answer)

The sum of 2 numbers is 9 and the sum of their squares is 53. The equation formed will be

  1. x2 + 9x - 14 = 0
  2. x2 + 9x + 14 = 0
  3. x2 - 9x - 14 = 0
  4. x2 - 9x + 14 = 0
  5. None of these
Question 15 Multiple Choice (Single Answer)

If a, b are roots of x2 + 7x + 12 = 0, find the equation whose roots are (a + b)2 and (a - b)2.

  1. x2 - 50x + 49 = 0
  2. x2 - 50x - 49 = 0
  3. x2 + 50x + 49 = 0
  4. x2 + 50x - 49 = 0
  5. None of these

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