Nonlinear Equations 2 — Advanced Math

Questions in this quiz (7)

1. $$\frac{x^2}{x^2-9}+\frac{3x}{x^2+3x}=\frac{1}{x-3}$$What value of $$x$$ satisfies the equation above?

   • $$-3$$
   • $$\frac{1}{3}$$
   • $$-1+\sqrt{13}$$
   • $$\frac{\sqrt{3}}{3}$$

2. $$(x-9)^2=16$$What is the sum of the solutions to the given equation?

   • $$5$$
   • $$13$$
   • $$15$$
   • $$18$$

3. Which quadratic equation has no real solutions?

   • $$x^2+10x-25=0$$
   • $$x^2-10x+25=0$$
   • $$2x^2+10x-25=0$$
   • $$2x^2-10x+25=0$$

4. $$\frac{1}{x^2+10x+21}=4$$If $$x$$ is a solution to the given equation, which of the following is a possible value of $$x+5$$?

   • $$-\frac{3}{2}$$
   • $$-\frac{\sqrt{17}}{4}$$
   • $$\frac{\sqrt{17}}{2}$$
   • $$\frac{9}{2}$$

5. $$-x^2-6x=k$$In the equation above, $$k$$ is a constant. If the equation has no real solutions, which of the following could be the value of $$k$$?

   • $$-6$$
   • $$-\frac{5}{2}$$
   • $$6$$
   • $$\frac{19}{2}$$

6. The first term of a sequence is $$3$$. Each term after the first is $$4$$ times the preceding term. If $$u$$ represents the $$k$$th term of the sequence, which equation gives $$u$$ in terms of $$k$$?

   • $$u=3(4^{k-1})$$
   • $$u=4(3^k)$$
   • $$u=3(4^k)$$
   • $$u=4(3^{k-1})$$

7. $$24x^2+(24b+a)x+ab=0$$In the given equation, $$a$$ and $$b$$ are positive constants. The product of the solutions to the given equation is $$kab$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$\frac{1}{12}$$
   • $$\frac{1}{24}$$
   • $$12$$
   • $$24$$