Question

Find all zeros and their multiplicities. f(x) = 7x^3+x

Answer 1

so first let f(x) = 0

so then

\[7x^3 + x = 0\]

factoring gives

\[x(7x^2 + 1) = 0\]

so 1 zero occurs when x = 0

to find the other zeros you need to solve

\[7x^2 + 1 = 0\]

you may need the general quadratic formula...

Answer 2

Thank you!

Answer 3

\[-b \pm \sqrt{b ^{2}-4ac}/2a\]

Answer 4

how would i do that?

Answer 5

well b = 0, a = 7 and c = 1

so

\[x = \frac{0 \pm \sqrt{0^2 - 4 \times 7 \times 1}}{2 \times 7}\]

which will give a complex root...

and each root has a multiplicity of 1

Answer 6

okie dokes got it. thank you again!