Question

find the polynomial f(x) that has the roots of -3, 5, of multiplicity 2

Answer 1

\[(x+3)^2 (x-5)^2 \]

Answer 2

how would you verify the zeros of f(x)

Answer 3

because @FoolForMath wrote it in factored form, isn't it obvious?

Answer 4

where does the multiplicity 2 come in

Answer 5

that's the number of times each factor appears (it's exponent)

Answer 6

ok i understand that but how do I verify the zeros?

Answer 7

solve this equation:
\[\large (x+3)^2 (x-5)^2=0\]
the solution(s) to that equation are your zeros.

Answer 8

stick in a -3 then stick in a 5. you see the equation holds true.

Answer 9

ok thanks so much