Question

Find all the zeros of the equation.

-4x4 - 44x2 + 3600 = 0

Answer 1

A. 5, -5, 6i, -6i

B. 5, 6i

C. 5, -5, 6i, 0

D. -5, -6i

Answer 2

divide every term by -4

so

\[x^4 + 11x^2 - 900 = 0\]

this is basically a quadratic

so you can do a substitution and let

\[x^2 = u\]

then you have the equation

\[u^2 + 11u - 900 = 0\]

this may make it easier for you to solve.

Answer 3

so i sub -4 in for u and divide?

Answer 4

nope... I've done the division... you have

\[x^4 + 11x^2 - 900 = 0\]

find some factors of -900 that add to 11... try -25 as 1.... you can find the other...

Answer 5

im confused? would it be D?

Answer 6

nope... just do some math and you'll get the solution...

Answer 7

it makes no sense to me i dont get how there getting the solutions

Answer 8

ok... so how many -25 in - 900...?

Answer 9

how many what ??

Answer 10

36

Answer 11

ok... so if you factorise your polynomial you have

\[(x^2 - 25)(x^2 + 36) = 0\]

you need to solve the quadratics

\[x^2 - 25 = 0\]

and

\[x^2 + 36 = 0\]

I'll let you do that.

Answer 12

Well i dont know the answer but
x^2-25 = 0
5^2 - 25 = 0
and
x^2 + 36 = 0
-6^2 +36 = 0

Answer 13

Im not sure what the answer would be.. A?

Answer 14

@jim_thompson5910 please help !!

Answer 15

if there are complex roots, then they ALWAYS come in conjugate pairs

Answer 16

so if you had 2i as a root, then -2i would automatically be another root

Answer 17

the only place where this happens is choice A, so you're correct

Answer 18

So it is A right? i did my work correctly to?

Answer 19

yes it looks good

Answer 20

thank you Jim

Answer 21

np