Question

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 5(x + 7)^2(x - 7)^3

Answer 1

Set each factor containing a variable equal to zero. Then solve for x. The multiplicity of each zero is the exponent of the factor that gave you that zero.

Answer 2

\[\Large 5(x + 7)^2(x - 7)^3 = 0\]means either
x+7=0
or
x-7=0.

The power 2 on (x+7) means it is a doubled zero. The power 3 on (x-7) means it's a tripled zero.

Answer 3

Long story short.

You have two factors: (x + 7) and (x - 7)

Those give you the zeros like so:
x + 7=0
x = -7
and
x - 7 = 0
x = 7

The zeros is the hardest part. Multiplicity can be found by the exponent of the factors.

(x + 7)² This is to the second power. This is the same as: (x + 7)(x + 7) So the multiplicity is 2.

(x - 7)³ This is to the third power. This is the same as: (x - 7)(x - 7)(x - 7). So the multiplicity is 3.

Make sense?

Answer 4

the multiplicites are your exponents basically

like if i said

(x-1)^3 your root is 1 and your multiplicites are 3 or is that 2 since you already counted the 1 once as a root?

anyhoo that is cuzz

(x-1)^3=(x-1) (x-1) (x-1) so the root 1 accurs 3 times.

Answer 5

5(x + 7)^2(x - 7)^3
Usually the outside numbers dont matter so you can have


(x + 7)^2(x - 7)^3
x=-7 and x=7

with like 5 multiplicites. I forget if you include the root or not. If not then it is 3

Answer 6

-7, multiplicity 2; 7, multiplicity 3

4, multiplicity 1; -7, multiplicity 3; 7, multiplicity 3

-7, multiplicity 3; 7, multiplicity 2

4, multiplicity 1; 7, multiplicity 1; -7, multiplicity 1

Answer 7

@timo86m

Answer 8

top one ?

Answer 9

\[5(x+7)^{2}(x-7)^{3}\]

Answer 10

?

Answer 11

http://tinyurl.com/lornbeach1

Answer 12

Solve for x over the real numbers:
\(5 (x-7)^3 (x+7)^2 = 0 \)
Divide both sides by 5:
\((x-7)^3 (x+7)^2 = 0\)
Split into two equations:
\((x-7)^3 = 0 or (x+7)^2 = 0\)
Take cube roots of both sides:
\(x-7 = 0\) or \((x+7)^2 = 0\)
Add 7 to both sides:
\(x = 7\) or\) \((x+7)^2 = 0\)
Take the square root of both sides:
\(x = 7 \)or \(x+7 = 0\)
Subtract 7 from both sides:
so \( x = 7\) or \(x = -7\)

Answer 13

for anyone needing the answer to this it's: -7 with a multiplicity of 2 and 7 with a multiplicity of 3 :)