# Which of the following describes the zeroes of the graph of f(x) = 3x^{6} + 30x^{5} + 75x^{4}?

-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) = 3x^{6} + 30x^{5} + 75x^{4}

Taking out 3x^{4} as common

f(x) = 3x^{4} (x^{2} + 10x + 25)

So we get

f(x) = 3x^{4} (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) = 3x^{6} + 30x^{5} + 75x^{4}?

-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) = 3x^{6} + 30x^{5} + 75x^{4}.

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