1

\$ - x^2 + bx - 676 = 0\$

In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?

A) 51

B) 50

C) 48

D) 41

2

\$ x^2 - ax + 12 = 0\$
In the equation above, a is constant, and a > 0. If the equation has two integer solutions, what is a possible value of a?

A) 7

B) 13

C) 8

D) All the above

3

\$ ( x - 1)^2 = - 4\$
How many distinct real solutions does the given equation have?

A) Exactly one

B) Zero

C) Exactly two

D) Infinitely many

4

\$ x^2 - 34x + c = 0\$

In the given equation, c is a constant. The equation has no real solutions if c > n. What is the least possible value of n?

A) 296

B) 282

C) 289

D) 298

5

\$ x(kx - 56) = - 16\$

In the given equation, k is an integer constant. If the equation has no real solution, what is the least possible value of k?

A) 57

B) 59

C) 45

D) 50

6

Find the solutions to \$\sqrt(2x + 1) + \sqrt(x) = 4\$.

A) \$19/2\$

B) \$9\$

C) \$9/2\$

D) \$2/3\$

7

Determine the roots of \$(x^2 + 1)/x = 3\$.

A) x = 2

B) x = 1

C) x = 0

D) x = -1

8

Find all real solutions to \$\sqrt(x + 3) - \sqrt(x) = 1\$.

A) x = 2

B) x = 1

C) x = \$1/2\$

D) x = -1

9

\$z^2 + 10z - 24 = 0\$ What is one of the solutions to the given equation?

A) (-2, 12)

B) (2, 12)

C) (2, -12)

D) (-2, -12)

10

\$5x^2 - 37x - 24 = 0\$ What is the positive solution to the given equation?

A) 8

B) 3

C) 37

D) \$3/5\$