Question

What are the zeroes of the function? What are their multiplicities?

= x4 – 4x3 + 3x2 (1 point)

Answer 1

f(x)= x4 – 4x3 + 3x2

Answer 2

x^4-4x^3+3x^2=0
Solve for x to find zeros. CAN U?

Answer 3

to find zeros
f(x)=0
x^4-4x^3+3x^2=0
SOLVE FOR X.

Answer 4

what is " ^" that symbol supposed to be?

Answer 5

and I don't know how to solve for x

Answer 6

try to factor f(x)

Answer 7

^ means raise to the power
saying x4 is ambiguous (it could mean x times 4). so say x^4 for \(x^4\)

Answer 8

so would the answer be The numbers –1 and –3 are zeroes of multiplicity 2; the number 0 is a zero of multiplicity 1?

Answer 9

or is that completely wrong?

Answer 10

i seriously have no idea how to do this... :/

Answer 11

do you know how to "factor out" x^2 from
\[f(x)= x^4 – 4x^3 + 3x^2\]

use this rule: (ab + ac) = a(b+c) (this is the opposite of distribute)
you get
\[ x^2(x^2-4x+3) \]

Answer 12

multiplicity means how many times a root is repeated

the roots are the numbers that make f(x) be 0

when you have
\[ x^2(x^2-4x+3)=0\]
which is the same as
\[ x\cdot x\cdot (x^2-4x+3) =0\]
if you replace x with 0, the whole thing becomes 0. so x=0 is a root
because x is repeated (you have x times x or x^2), 0 has multiplicity 2

now you have to find the 2 roots that make \(x^2-4x+3=0\)

Answer 13

would it be The numbers 0 and 1 are zeroes of multiplicity 2; the number 3 is a zero of multiplicity 1?

Answer 14

The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1

Answer 15

no. First, this polynomial has a highest power of 4. that means you will have 4 roots
as explained above, 0 is repeated, so 2 of the roots are 0,0 or just 0 with multiplicity 2

there are 2 more roots to find

Answer 16

he number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1

Yes. I assume you guessed? you can check by replacing x with 1 in the equation. If you get 0 then you know 1 is a root.

to solve for these roots, you factor
x^2 -4x+3=0

Answer 17

See http://www.khanacademy.org/math/algebra/polynomials/v/factoring-quadratic-expressions
for how to do this if you don't know how