Question

Of the following statements, how many are true?

-A quartic polynomial can have exactly one imaginary root.
-A cubic polynomial must have a real root.
-A quadratic polynomial can have no real roots
-A polynomial can have no real roots

Answer 1

@FibonacciChick666

Answer 2

So, what do you know about imaginary roots?

Answer 3

they come in pairs

Answer 4

exactly, so can 1 be true?

Answer 5

I don't think that first one is true. I know the second and third one is true. but I'm not sure if the fourth one is true?

Answer 6

correct, the first is false

Answer 7

if a quadratic polynomial can have no real roots, why can't a generic polynomial?

Answer 8

is a quadratic, not a polynomial?

Answer 9

yes but would it look like this

Answer 10

yea, something like that

Answer 11

so it doesn't have to have an real roots?

Answer 12

so the 2, 3, and 4 statement are correct.

Answer 13

yep

Answer 14

take \((x^2+1)=0\) There are no real roots

Answer 15

okay thank you very much. I get it now!

Answer 16

but by the fundamental theorem of algebra, we know that there must be as many roots as the degree of the polynomial. So in that case, there are 2 complex(imaginary) roots

Answer 17

np!

Answer 18

If x^8 has only 2 real roots and x^9 has three real roots how does this work?

Answer 19

well, the rest are either multiples or imaginary pairs

Answer 20

note, I didn't say distinct roots, just that there are roots