Instructions:

Solve the following equations and find the real roots. Provide your final answer in the space provided.

Questions:

1) Find the real roots of the equation:

• $\frac{9}{x^4}+\frac{8}{x^2}=1$

Answer: _______________________

2) Solve:

• $x^4-13x^2+36=0$

Answer: _______________________

3) Find the real roots of the equation:

• $x^2-2=\frac{8}{x^2}$

Answer: _______________________

4) Solve:

• $x^6-7x^3-8=0$

Answer: _______________________

5) Solve:

• $2x^4-11x^2+5=0$

Answer: _______________________

6) Solve the equation:

• $\frac{9}{x^4}+\frac{5}{x^2}=4$

Answer: _______________________

7) Solve:

• $2x-9\sqrt{x}+10=0$

Answer: _______________________

8) Solve:

• $\sqrt{x}(\sqrt{x}+1)=6$

Answer: _______________________

9) Find the x-coordinates of points A and B where the curve $y=2\sqrt{x}$ and the line $3y=x+8$ intersect.

Answer: _______________________

10) Find the values of $a$, $b$, and $c$ for the quadratic equation $y=a{x}^2+bx+c$, given that the graph crosses the x-axis at $(1,0)$ and $(\frac{49}{4},0)$ and meets the y-axis at $(0,7)$.

Answer: a = __________, b = __________, c = __________

Answer Key:

• 1) $x=3$ or $x=-3$
• 2) $x=\pm 3$ or $x=\pm 2$
• 3) $x=2$ or $x=-2$
• 4) $x=2$ or $x=-1$
• 5) $x=\pm \sqrt{5}$ or $x=\pm \frac{\sqrt{2}}{2}$
• 6) $x=\frac{3}{2}$ or $x=-\frac{3}{2}$
• 7) $x=6.25$ or $x=4$
• 8) $x=4$
• 9) $x=16$ and $x=4$
• 10) $a=\frac{4}{7},b=-\frac{53}{7},c=7$