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

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

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

### A quadratic function f(x) attains a maximum of 3 at x = 1

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

### If both a and b belong to the set {1, 2, 3, 4}, then the number of equations

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

### Let p and q be the roots of the quadratic equation x^2 - (α-2)x - α - 1 = 0

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

### The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0

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

### One root of x^2 + kx - 8 = 0 is square of the other. Then the value of k is

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

### What is the value of m which satisfies 3m^2 - 21m + 30

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

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

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

### The minimum possible value of the sum of the squares of the roots

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