Question

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

f(x) = 4(x + 7)^2 (x - 7)^3

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

B. -7, multiplicity 3; 7, multiplicity 2

C. 4, multiplicity 1; 7, multiplicity 1; -7, multiplicity 1

D. -7, multiplicity 2; 7, multiplicity 3

Answer 1

Do you know what to do here?

Answer 2

Leave that 4 alone. We just have to look at stuff like \(\rm x + blah\) or \(\rm x - blah\).

Answer 3

If one factor is \(\rm x + blah\), then \(\rm -blah\) is one of the roots. If one factor is \(\rm x - blah\), then \(\rm +blah\) is one of the roots.

Answer 4

If your factor is written like \(\rm (x - blah)^{\text{blah exponent}}\), then \(\rm blah\) is the root and \(\text{blah exponent}\) is the multiplicity.

Answer 5

Let's have an example.\[\rm blahfunction(x) = (x - 3)^2(x + 7)^{12832838343}\]The roots are \(3\) and \(-7\) with multiplicity \(2\) and \(12832838343\) respectively. :P

Answer 6

Whew, that is some serious multiplicity you got there, Parth.