Quadratic Equations

1

Largest value of min(2 + x2, 6 - 3x), when x > 0, is

  1. 1
  2. 2
  3. 3
  4. 4
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2

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

  1. -180
  2. -159
  3. -110
  4. -119
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3

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax2+ bx + 1 = 0 having real roots is

  1. 6
  2. 7
  3. 10
  4. 12
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4

Let p and q be the roots of the quadratic equation x2 - (α - 2)x - α - 1 = 0. What is the minimum possible value of p2 + q2?

  1. 0
  2. 3
  3. 4
  4. 5
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5

The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is

  1. 0
  2. 1
  3. 2
  4. 3
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6

One root of x2 + kx - 8 = 0 is square of the other. Then the value of k is

  1. 2
  2. -2
  3. 8
  4. -8
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7

What is the value of m which satisfies 3m2 - 21m + 30 < 0?

  1. m < 2 or m > 5; 2 < m < 5
  2. 2 < m < 5
  3. m < 2 or m > 5
  4. m > 2
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8

Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all?

  1. 0 ≥ x ≥ –2
  2. 0 ≤ x ≤ 2
  3. –1 ≥ x ≥ –2
  4. 1 ≤ x ≤ 2
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9

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

  1. 1
  2. 2
  3. 3
  4. 4
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