Question

which of the following describes the zeroes of the graph of f(x) = 3x6 30x5 75x4? –5 with multiplicity 2 and 1/3 with multiplicity 4 5 with multiplicity 2 and 1/3 with multiplicity 4 –5 with multiplicity 2 and 0 with multiplicity 4 5 with multiplicity 2 and 0 with multiplicity 4

Answer 1

factor
when it repeats, the multipicty is how many times it repeats
roots are (x-r1) wher r1 is a root


f(x)=3(x-0)^4(x-(-5))^2

0 multiplicity 4 and -5 multiplicty 2
3rd option

Answer 2

The roots of f(x) are " 0 with multiplicity 4" and " -5 with multiplicity 2".

Explanation:

we are given a polynomial function as:

`f(x)=3x^6+30x^5+75x^4`

which can also be written as:

`f(x)=3x^4(x^2+10x+25)\\\\\\f(x)=3x^4(x^2+5x+5x+25)\\\\f(x)=3x^4(x(x+5)+5(x+5))\\\\f(x)=3x^4(x+5)(x+5)`

for finding the roots of the polynomial equation we have to equate f(x)=0.

we get the possible roots of x as '0' with multiplicity '4' and '-5' with multiplicity '2'.