How do you find the zeroes of f(x)=x4=−7x2−144?

1 Answer
Gió
Jul 20, 2015

I found:
x1=4
x2=−4
x3=3i
x4=−3i

Explanation:

I start supposing that the second = sign is not necessary, so:
f(x)=x4−7x2−144
You can find the zeroes (x values that makes your function equal to zero) by setting your function equal to zero and get:
x4−7x2−144=0

set x2=u so you get:
u2−7u−144=0
Using the Quadratic Formula you get:
u1,2=7±√49−4(−144)2=7±252
so you get 2 solutions:
u1=16
u2=−9
But x2=u so x=±√u

You get 4 zeroes for your function (2 Real and 2 Immaginary):
x1=√16=4
x2=−√16=−4
x3=√−9=3i
x4=−√−9=−3i

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