Is this right?

Question

find a cubic polynomial function f that satisfies the given conditions

rational zero 1/2, irrational zeros 1 + sqr(3) and 1 - sqr(3), coefficient of x is 2

*sqr = square root*

Answer: 2 ( x - 1 - sqr(3)) (x - 1 + sqr(3)) (x - (1/2)) ??

thanks for your help

Answer 1

Not really. We can not assume that multiplier is 2!

Write
(1) A ( x - 1 - sqr(3)) (x - 1 + sqr(3)) (x - (1/2)), expand.

2) You will get a cubic that looks like

A*a x^3 + A*b x^2 + A*c x + A*d*n

and you want Ac = 2 or

A = 2/c. That's the multiplier that will work.

Good luck.

Answer 2

Yes, that is correct. You could make it a little nicer as:
( x - 1 - sqr(3)) (x - 1 + sqr(3)) (2x-1)