SOLUTION: 1.) What is a polynomial function in standard form of degree 4 with zeros: -1, 2, 5i? 2.) Given f(x)=5x+1 Find f^-1(x) & verify the answer is correct by showing that (fo

Question 117426: 1.) What is a polynomial function in standard form of degree 4 with zeros: -1, 2, 5i?
2.) Given f(x)=5x+1
Find f^-1(x) & verify the answer is correct by showing that (fof^-1)(x)=x
3.) solve: a) log (x+4) - log 2x=0
b) 2ln x + 5 = 7
4.) Find all the zeros of the polynomial function: P(x)=2x^4+3x^3+16x^2+27x-18 then write the P(x) as a product of its linear factors.

Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
1.) For any polynomial equation with real coefficients, complex roots occur in conjugate pairs.
So, if 5i i.e. (0 + 5i) is a root then (0 - 5i) is the other root.
Hence, the 4 zeros are x = -1, 2, 5i, - 5i
Hence the polynomial is

=
=
=
=
=
2.)
f(x) = 5x + 1
5x = f(x) - 1

Hence,

Verification:

3.a)

3.b)

4.) Try yourself!
RELATED QUESTIONS
Write a polynomial function of minimum degree with real coefficents whose zeros include... (answered by jsmallt9)

Find a polynomial function f(x) of the indicated degree with integer coefficients that... (answered by Fombitz)

Find a polynomial function f(x) of the indicated degree with integer coefficients that... (answered by MathLover1)

Form a polynomial f(x) with real coefficients having the given degree and zeors. Degree... (answered by Edwin McCravy)

Form a polynomial f(x) with real coefficients having the given degree and zeros.... (answered by Alan3354)

Form a polynomial f(x)with real coefficients having the given degree and zeros. Degree 5... (answered by tommyt3rd)

form a polynomial f(x) with real coefficients having the given degree and zeros.... (answered by jsmallt9)

Write a polynomial function in standard form with the given zeros. x= 1,-1, -2 (answered by jsmallt9)