How to Construct Specific Degree 3 Polynomials with Given Conditions?

[Mathman23]

Urgent: n-degree polynomial problems

Hi

I know I have asked this before, but I haven't been able to solve the problem using the tools that I have.
Let me recap

I have been tasked to find two polynomials of degree 3 p(x) and q(x) complies with the following conditions.

p( - 1) = 1 , p'(-1) = 0 , q(1) = 3, q'(1) = 0, p(0) = q(0), p'(0) = q'(0)

I'm told that the resulting two polynomials of degree 3 are:

p(x) = (2 + s - 2t) x^3 + (3 + 2s - 3t) x^2 + s*x + t

q(x) = (-6 + s + 2t) x^3 + (9 - 2s - 3t) x^2 + s*x +t

where s,t belong to R.

I have looked through my linear algebra text-book several times, but can't find a method on howto build polynomials which resemble p(x) and q(x).

Is there anybody who can direct me to a method on howto build the to above polynomials ?

Sincerley and Best Regards,

Fred

p.s. Thanks again for all Your answers in the past they mean the world to me :-)

p.p.s. I have done some research now and s, t are the socalled roots of the the cubic polynomial.

 

[Muzza]

Suppose p(x) = ax^3 + bx^2 + cx + d and q(x) = ex^3 + fx^2 + gx + h. Use the other information given to create a linear system of equations with the coefficients of p and q as variables.

 

[Mathman23]

Hi and thanks for Your answer,

The equations inside the parantheses are they derived from the system of linear equation?

Hi I'm told that all this has something to do with vector spaces. But exactly how I'm a bit unsure of :-(

Sincerley and Best Regards,

Fred

Suppose p(x) = ax^3 + bx^2 + cx + d and q(x) = ex^3 + fx^2 + gx + h. Use the other information given to create a linear system of equations with the coefficients of p and q as variables.

 

[Mathman23]

My problem is that first of all my Linear Algebra textbook doesn't deal with these kinds of polynomials.
Futher I need to present the calculations on friday if I can't I fail.

Hope there is somebody who can direct me on howto obtain the final solution for this problem ? :-)

Thank You and God Bless You all.

Sincerely
Fred

Hi

I know I have asked this before, but I haven't been able to solve the problem using the tools that I have.
Let me recap

I have been tasked to find two polynomials of degree 3 p(x) and q(x) complies with the following conditions.

p( - 1) = 1 , p'(-1) = 0 , q(1) = 3, q'(1) = 0, p(0) = q(0), p'(0) = q'(0)

I'm told that the resulting two polynomials of degree 3 are:

p(x) = (2 + s - 2t) x^3 + (3 + 2s - 3t) x^2 + s*x + t

q(x) = (-6 + s + 2t) x^3 + (9 - 2s - 3t) x^2 + s*x +t

where s,t belong to R.

I have looked through my linear algebra text-book several times, but can't find a method on howto build polynomials which resemble p(x) and q(x).

Is there anybody who can direct me to a method on howto build the to above polynomials ?

Sincerley and Best Regards,

Fred

p.s. Thanks again for all Your answers in the past they mean the world to me :-)