1. The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.

3. If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . According to this model, by how much will the value of this piece of property increase between the years 2007 and 2008?

4. Solve loga (7x +1) = loga (4x +16).

5. Find the domain of f (x) = 7 + 3x + 21 , and express it using interval notation.

6. If points A, B, and C lie on a coordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coordinates for point C satisfy(ies) d(A, C) < d(B, C)?

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1. The degree three polynomial f(x) with real coefficients and leading
coefficient 1, has -3 and + 4i among its roots. Express f(x) as a
product of linear and quadratic polynomials with real coefficients.

The complex conjugate of +4i must be a root to the polynomial too.
So the polynomial has three roots: r1 = -3, r2 = +4i, r3 = -4i.
The leading coefficient a = 1.
The polynomial is

2. Find the inverse of the function f(x) = x1/3 + 2.

We need ...

Solution Summary

Polynomials with real and complex solutions are investigated. The solution is detailed and well presented.

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... the given polynomial will have only complex roots. ... one needs to analyze the polynomial function where ( 1 ... the equation admits always at least one real solution. ...

...Polynomial. By:- Thokchom Sarojkumar Sinha. Let be a field of real numbers. Prove that is a field isomorphic to the field of complex numbers. Solution:- Let be ...

... answer with the help of one of the identities of factorization of polynomials. ... Is the result real, complex, or both? ... Neat and step-wise solutions are provided. ...

... f(x)=x3-5x2+16x-30 Use the complex zeros to write f in factored form f(x ... 6. Use the rational theorem to find all the real zeros of the polynomial function. ...

... is an automorphism of that interchanges the complex conjugate roots # and " and fixes the real roots ... Find a polynomial of degree 7 over ℚ whose Galois ...

... Step 1: Multiply the complex numbers in the ... on multiplying polynomials, go to Tutorial 6: Polynomials. ... Add real numbers together and imaginary numbers together ...

... Any polynomial equation has n complex roots, in general, in ... axis is set up where the real number is ... The complex number system is defined and supplemented with ...

... P into linear and irreducible quadratic factors with real coefficients. ... 12 = (x-3)(x^2+4). The polynomial (x^2 ... and x^2+16 is irreducible over reals, because its ...

... All variables represent positive real numbers. 14. Solution. ... So, there are two complex solutions: x=4+i and x=4-i. ... Evaluate each polynomial as indicated. ...