Round 62.686 to the nearest hundredth
2 answers:
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If -3+5i is a solution, then by the conjugate root theorem, -3-5i is also a solution. We find the polynomial by multiplying together the factors. If x = -4, then x + 4 is the factor. If x = -3+5i, then (x-(-3+5i)) is a factor, and so is (x-(-3-5i)). Simplifying those down gives us as the first factor as (x+3-5i) and the second as (x+3+5i). We can FOIL those 2 together to get their product, and then FOIL in x+4. FOILing the 2 complex factors together gives us . If we combine like terms and cross out things that cancel it's much easier than what it looks like there! It simplifies down to
. Since i^2 = -1, it simplifies further to
and finally, to
. Now we will FOIL in x+4.
. Our final simplified third degree polynomial is
Answer:
= - 21
+ 6x² + 1
Step-by-step explanation:
Differentiate each term using the power rule
(a
) = na
Given
y = - 3 + 2x³ + x , then
= (7 × - 3 )
+ (3 × 2)x² + (1 × 1 )
= - 21 + 6x² + 1