How do I derive polynomial using given roots?

Given the known roots -2 -0.5 2 4.5

I am asked to define a symbolic variable 'x'

and derive the symbolic polynomial for the given roots

I have searched google several times to no avail, can anyone help me with this?

Answer 1

[Andrei Bobrov]

v = [-2 -0.5 2 4.5]
x= sym('x')
yourpoly = expand(prod(x-v))

[Gollapapani]

Can it also deal with complex roots?

[Steven Lord]

Try it!

r = [-1 1+3i 1-3i];
x = sym('x');
yourpoly = expand(prod(x-r))

yourpoly = 

check = solve(yourpoly)

check = 

Looks good to me. [Yes, the elements in check are in a different order than they appear in r. This is not a bug.]

Another approach, if you want to do this numerically, is to use the poly function in MATLAB. This returns the vector of coefficients, but we can write it as an expression in the symbolic variable using poly2sym.

p2 = poly(r)

p2 = 1×4

1 -1 8 10

yourpoly2 = poly2sym(p2, x)

yourpoly2 = 

Let's make sure the two results are the same.

check = isAlways(yourpoly == yourpoly2)

check = logical
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