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Solve for x: x4 - 21x2 - 35 = 65
Example
Solution
Step 1 Write the equation in standard form.
Subtract 65 from both sides.
Step 2 Factor.
Step 3 Use the Zero Product Property.
Step 4 Solve for the variable.
x4 - 21x2 - 35
x4 - 21x2 - 100
(x2
+ 4)(x2 - 25)
x2 + 4 = 0 or x2
-25
x2 = - 4 or x2
= 65
= 0
= 0
= 0
= 25
So, there are four solutions: -2i, +2i, -5, and +5.
The equation x4 - 21x2 - 35 = 65 written in standard form is x4 - 21x2 - 100
= 0. The graph of the corresponding function,
f(x) = x4 - 21x2 - 100 is shown.
The graph crosses the x-axis at only two locations, x = -5 and x
= 5. This is because these are the only real number solutions.
