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

Solution:

It is given that

f(x) = 3x⁶ + 30x⁵ + 75x⁴

Taking out 3x⁴ as common

f(x) = 3x⁴ (x² + 10x + 25)

So we get

f(x) = 3x⁴ (x + 5)²

So the zeros of the function are

x = -5 with multiplicity 2

x = 0 with multiplicity 4

Therefore, the zeros of the graph are -5 with multiplicity 2 and 0 with multiplicity 4.

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

Summary:

-5 with multiplicity 2 and 0 with multiplicity 4 describes the zeroes of the graph of f(x) = 3x⁶ + 30x⁵ + 75x⁴.