Question

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

Answer 1

Roots essentially mean where x intersects the x-axis or where y=0
x=-2
x=3 multiplicity 2
for x=-2, you can do (x+2) = f(x)
for x = 3, you can do (x-3) = f(x)
for multiplicities, you simply have to raise the power
for x=3 multiplicity 2, you do (x-3)^2 = f(x)
Combine these to get your equation:
\[f(x) = (x+2)(x-3)^2\]
multiply and simplify to get your polynomial

Answer 2

Thank you so much!