Question

What are the possible positive, negative, or complex possibilities of 4x^3-9x^2-7x-6

Answer 1

Do you know the rational root theorem?

Answer 2

No I'm new to this. I just want the answer so I can do the others

Answer 3

x=3

Answer 4

then you can solve that and find complex roots.

Answer 5

huh

Answer 6

\( f(3)=0 \)

Answer 7

So 0 for positive?

Answer 8

nope, what's between in the brackets of f(x) is what you insert into the function, therefore 3 is a positive, real root.

Answer 9

Yes but I need the positive, negative, and compleex possible roots

Answer 10

then you will get as a quadratic polynomial
\( f(x) = 4x^2+3x+2\) there you only have complex roots.

Answer 11

No negatives?

Answer 12

hmm yes negative complex roots, but no real negative roots

Answer 13

for the complex roots you will get:
\( \\ \large x_1 = \frac{1}{8}(-3-i\sqrt{23})\)

Answer 14

and therefore also it's complex conjugate.

Answer 15

compare the given equation with \[a {x ^{2}} + b y^{2}+c\]

Answer 16

How many total zeros

Answer 17

three, it is a polynomial of third degree.

Answer 18

therefore three roots in \(\mathbb{C}\)

Answer 19

So there's 3 complex

Answer 20

nope, the complex numbers include the reals, it's a higher set of numbers.

One root \( \in \mathbb{R}\) and two roots \( \in \mathbb{C}\)

Answer 21

Nevermind -____-

Answer 22

where's the problem?

Answer 23

now substitute the values of a,b,c in th equation below\[[-b+\sqrt{(b ^{2}-4a.c)} ]\div2.a\]

Answer 24

well done @mbibin91, by the way, if you don't already know, if you want a nice clean multiplication dot, use \cdot in LaTeX

Answer 25

There's 1 positive
2 or 0 negative
and 2 or 0 complex

Answer 26

@Spacelimbus
k :)

Answer 27

1 positive, 0 negative (in reals) and 2 complex