Question

12) f(x) = x4 + 25x2 +144? A) f(x) = (x + 3i)(x - 3i)(x + 4i)(x - 4i) C) f(x) = (x + 1)(x - i)(x + 12i)(x - 12i) B) f(x) = (x + 3 + 412(x + 3 - 4i)2 D) f(x) = (x + 3i)?(x + 4i)2

Answer 1

we have

f(x) = x4 + 25x2 +144

using a graphing tool

The equation has no real solutions

so

Verify each possible solution

Option A

we have

f(x)=(x+3i)(x-3i)(x+4i)(x-4i)

Applying difference of squares

f(x)=(x^2-9i^2)(x^2-16i^2)

REmember that

i^2=-1

substitute

f(x)=(x^2+9)(x^2+16)

Apply distributive property

f(x)=x^4+16x^2+9x^2+144

Combine like terms

f(x)=x^4+25x^2+144

therefore

the answer is the option A