State the possible number of imaginary zeros of f(x)=7x3-x2+10x-4?

Question

The problem is f(x)= 7x(cubed) - x(squared) +10 x - 4

Choices for answer:

exactly 1
exactly 3
3 or 1
2 or 0

Answer 1

D ( 2 or 0)

This is because the coefficients of the given cubic polynomial are real numbers and so any real zero needs be accompanied by its complex conjugate and so as stated earlier MUST come in pairs so either there are 2 or there cannot be any.

Answer 2

2 or 0

Answer 3

A 3rd grad polynomials has up to 3 real roots, but they are exactly 3 if you consider real an complex root.

Any 3rd grad polynomials tends to -oo when x tends to -oo and grows to +oo if x tends to +oo, then, at some point, being a contious function, it must be 0.

The quotient is a quadratic equation, so, you can have 2 different real roots, 1 double real root (in which case, the number of the complex roots will be 0), or 2 complex roots

So, the answer is 2 or 0

Ana

Answer 4

imaginary numbers occur in pairs. This is so because coefficients are real.

So number of imaginary roots 0 or 2

Answer 5

There will be at least 1 real root. There will be either 2 complex roots or none.
Answer is 2 or zero.

Answer 6

it would be 2 or 0, because imaginary numbers always come in conjugate pairs

Answer 7

2 or 0. And they may not be pure imaginary, they may also be complex.


Doug