1
###
If the roots of the equation (a2 - bc)x2 + 2(b2 - ac)x + (c2 - ab) = 0 are equal

If the roots of the equation (a^{2} - bc)x^{2} + 2(b^{2} - ac)x + (c^{2} - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

- a
^{3}+ b^{3}+ c^{3}= 0 - a
^{3}+ b^{3}+ c^{3}= 3abc - a
^{2}+ b^{2}+ c^{2}= 0 - a + b + c = abc

2
###
If α and β are the roots of the equation x^2 - x - 1 = 0

If α and β are the roots of the equation x^{2} - x - 1 = 0, then what is (α^{2} + β^{2})/((α^{2} - β^{2})(α - β))

- 2/5
- 4/5
- 3/5
- 1/5

3
###
If x^2 = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values

If x^{2} = 6 + √(6 + √(6 + √(6 +....∞)), then what is one of the values of x equal to?

- 3
- 4
- 5
- 6

4
###
The expression 2x^3 + x^2 - 2x - 1 = 0 is divisible by

The expression 2x^{3} + x^{2} - 2x - 1 = 0 is divisible by

- 2x - 1
- 2x + 1
- x + 2
- x - 2

5
###
In solving a problem, one student makes a mistake in the coefficient

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:

- x
^{2}+ 10x + 9 = 0 - x
^{2}- 10x + 16 = 0 - x
^{2}- 10x + 9 = 0 - x
^{2}+ 10x + 16 = 0

6
###
The sign of the quadratic polynomial ax^2 + bx + c is always

The sign of the quadratic polynomial ax^{2} + bx + c is always positive if

- a is positive and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≥ 0. - a is positive and b
^{2}- 4ac ≥ 0.

7
###
If a - b = 4 and a^2 + b^2 = 40 where a and b are positive integers

If a - b = 4 and a^{2} + b^{2} = 40 where a and b are positive integers, where a and b are positive integers, then a^{3} + b^{6} is equal to

- 264
- 280
- 300
- 324

8
###
If the roots of the equation Ax^2 + Bx + C = 0 are -1 and 1

If the roots of the equation Ax^{2} + Bx + C = 0 are -1 and 1, then which one of the following is correct?

- A and B are both positive
- A and C are both negative
- A and C are of opposite sign
- A and C are both zero

9
###
The value of x^2 - 4x + 11 can never be less than

The value of x2 - 4x + 11 can never be less than

- 7
- 8
- 11
- 22

10
###
Aman and Alok attempted to solve a quadratic equation. Aman made a mistake

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

- –4, –3
- 6, 1
- 4, 3
- –6, –1

11
###
If α and β are the roots of the equation x^2 + px + q = 0

If α and β are the roots of the equation x^{2} + px + q = 0, then what is α^{2} + β^{2} equal to?

- p
^{2}– 2q - q
^{2}– 2p - p
^{2}+ 2q - q
^{2}– q