Quadratic Equations

1

If p and q are the roots of the equation x2 + px + q = 0, then

  1. p = 1, q = -2
  2. p = -2, q = 1
  3. p = -2, q = 0
  4. p = 0, q = 1
2

If a and b are the roots of the equation x2 - x + 1 = 0, then a2009 + b2009 is equal to

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

The equation esinx – e-sinx – 4 = 0 has

  1. Infinite number of real roots
  2. No real roots
  3. Exactly one real root
  4. Exactly four real roots
4

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

  1. x2 + 18x + 16 = 0
  2. x2 - 18x - 16 = 0
  3. x2 - 18x + 16 = 0
  4. x2 + 18x - 16 = 0
5

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

  1. 18 months
  2. 19 months
  3. 20 months
  4. 21 months
6

If α ≠ β but α2 = 5α - 3 and β2 = 5β - 3, then the equation having α/β and β/α as its roots is

  1. 3x2 - 19x - 3 = 0
  2. 3x2 - 19x + 3 = 0
  3. x2 - 5x + 3 = 0
  4. 3x2 + 19x - 3 = 0
7

Let a and b be roots of the equation px2 + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

  1. 2√17 / 9
  2. √61 / 9
  3. √34 / 9
  4. 2√13 / 9
8

If a, b, c are distinct +ve real numbers and a2 + b2 + c2 = 1, then ab + bc + ca is

  1. greater than 1
  2. equal to 1
  3. less than 1
  4. any real number
9

If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0, then its roots are

  1. 0, -1
  2. 1, 1
  3. 0, 1
  4. 2, 1
10

What is the sum of the squares of the roots of the equation x2 + 2x - 143 = 0?

  1. 170
  2. 180
  3. 190
  4. 290
11

If the difference between the roots of ax2 + bx + c = 0 is 1, then which one of the following is correct?

  1. b2 = a(a + 4c)
  2. a2 = b(b + 4c)
  3. a2 = c(a + 4c)
  4. b2 = a(b + 4c)
12

If α and β are the roots of the equation x2 - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?

  1. 1 - r
  2. q - r
  3. 1 + r
  4. q + r