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Solve for coefficients
Select Solve poly… Enter vector of roots

Press to return to stack. The stack will show the following results in ALG

mode`(the same result would be shown in RPN mode):

All the solutions are complex numbers: (0.432,-0.389), (0.432,0.389), (- 0.766, 0.632), (-0.766, -0.632).

Generating polynomial coefficients given the polynomial's roots

Suppose you want to generate the polynomial whose roots are the numbers [1, 5, -2, 4]. To use the calculator for this purpose, follow these steps:

˜„Ô15@SOLVE@PressϘ˜í2\to return‚í@@OK@@to stack,4the@@OK@@coefficients will be shown in the stack.

Press `to trigger the line editor to see all the coefficients.

˜

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HP 49g manual