\$57"x"^2 + (57"b" + "a")"x" + "ab" = 0\$
In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab , where is k a constant. What is the value of k?

A) 19

B) \$1/(57)\$

C) 57

D) \$1/(19)\$

\$"x"^2 - 2"x" - 9 = 0\$
One solution to the given equation can be written as \$1 + \sqrt("k")\$, where k is a constant. What is the value of k?

A) 25

B) 10

C) 20

D) 30

If \$3"x"^2 - 18"x" - 15 = 0\$, what is the value of \$"x"^2 - 6"x"\$?

A) 8

B) 10

C) 12

D) 5

\$ ("x"^2) /(\sqrt("x"^2 - "c"^2)) = ("c"^2)/(\sqrt("x"^2 - "c"^2) ) + 39\$
In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation?

A) \$ \sqrt("c"^2 + 39^2)\$

B) \$- \sqrt("c"^2 - 39^2)\$

C) \$ \sqrt("c"^2 - 39^2)\$

D) \$- \sqrt("c"^2 + 39^2)\$

\$ (4"x"^2)/("x"^2 - 9) - (2"x")/("x" + 3) = 1/("x" - 3)\$
What value of x satisfies the equation above?

A) \$- 1/2\$

B) -3

C) \$1/2\$

D) 3

Which of the following equations has exactly ONE real number solution?

A) \$\sqrt("x"^2 + 1) = 2\$

B) \$"x"^3 - 4"x" = 0\$

C) \$2^"x" - 3 = 0\$

D) sin(x) + cos(x) = 1

Find the solutions to \$\sqrt("x" + 2) + \sqrt("x") = 3\$.

A) \$"x" = 49/36\$

B) \$"x" = 36/49\$

C) \$"x" = 39/46\$

D) \$"x" = 46/39\$

Determine the roots of \$("x"^2 - 1)/"x" = 2\$.

A) \$"x" = 1 + \sqrt(2)\$, \$"x" = 1 - \sqrt(2)\$

B) \$"x" = 2 + \sqrt(-2)\$, \$"x" = 2 - \sqrt(-2)\$

C) \$"x" = 1 + \sqrt("x"^2)\$, \$"x" = 1 + \sqrt("x"^2)\$

D) \$"x" = 2 + \sqrt(-2)\$, \$"x" = 1 + \sqrt(-2)\$

Find all real solutions to \$(1/"x"^2) - 2"x" + 1 = 0\$.

A) x = \$11/2\$

B) x = 1

C) x = 4

D) x = 2i

\$1/("x"^2 + 10"x" + 25) = 4\$
If x is a solution to the given equation, which of the following is a possible value of x + 5?

A) \$5/2\$

B) \$1/2\$

C) \$11/2\$

D) \$9/2\$