About Solving Equations that are Quadratic in Form:
We will encounter non-quadratic equations that are quadratic in form. We can create a quadratic equation by making a simple substitution. We can then solve the quadratic equation using the quadratic formula. When done, we substitute once more to obtain a solution in terms of the original variable involved.
Test Objectives
- Demonstrate the ability to identify a non-quadratic equation which is quadratic in form
- Demonstrate the ability to use substitution to create a quadratic equation
- Demonstrate the ability to solve an equation which is quadratic in form
#1:
Instructions: Solve each using the quadratic formula.
a) $$12x^4 + 7x^2 - 45=0$$
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#2:
Instructions: Solve each using the quadratic formula.
a) $$25x^4 - 10x^2 - 3=0$$
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#3:
Instructions: Solve each using the quadratic formula.
a) $$3x^\frac{2}{5}- 7x^\frac{1}{5}+ 2=0$$
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#4:
Instructions: Solve each using the quadratic formula.
a) $$(7x^2 - 51)^2 - 8(7x^2 - 51) - 48=0$$
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#5:
Instructions: Solve each using the quadratic formula.
a) $$5x^\frac{2}{3}+ 7x^\frac{1}{3}- 6=0$$
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Written Solutions:
#1:
Solutions:
a) $$x=\pm \frac{\sqrt{15}}{3}\hspace{.5em}or \hspace{.5em}x=\pm\frac{3i}{2}$$
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#2:
Solutions:
a) $$x=\pm\frac{\sqrt{15}}{5}\hspace{.5em}or \hspace{.5em}x=\pm\frac{i\sqrt{5}}{5}$$
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#3:
Solutions:
a) $$x=32 \hspace{.5em}or \hspace{.5em}x=\frac{1}{243}$$
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#4:
Solutions:
a) $$x=\pm3 \hspace{.5em}or \hspace{.5em}x=\pm\frac{\sqrt{329}}{7}$$
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#5:
Solutions:
a) $$x=-8 \hspace{.5em}or \hspace{.5em}x=\frac{27}{125}$$