Question

What is the multiple zero and multiplicity of f(x)=x^3-14x^2+49x

Answer 1

Multiplicty is how many times a root or zero repeats
example

f(x)=(x-r1)(x-r2)² wold be
zeroes are r1 multiplicity 1 an r2 multiplity 2


so

f(x)=x(x^2-14x+49)
f(x)=(x)(x-7)^2
roots are 0 multipliicty 1 and 7 multilicty 2

so it would be B

Answer 2

X^3 - 14x^2 + 49x = 0

Factor an x out:

x(x^2 - 14x + 49) = 0

Find two factors of 49 that add to -14 (-7 and -7). Convert the trinomial to two binomials:

x(x - 7)(x - 7) = 0

The zeros are:

x = 0 and x = 7.

7 occurs as a zero twice and therefore has a multiplicity of 2.