Question

Which of the following polynomials has the lowest degree, a leading coefficient of 2, and 1/2 and 3 + √5 as roots?

Answer 1

do you have to make up that polynomial or pick it from a list ?

Answer 2

@phi it is opened ended

Answer 3

@amistre64

Answer 4

@phi

Answer 5

@ganeshie8

Answer 6

if you have roots a and b then you can write
(x-a)(x-b) and expand it if you like
if you want the x^2 term to have a coefficient of 2, write
2(x-a)(x-b)

that will work for your roots 1/2 and 3 + √5
however, it will produce a polynomial with irrational (i.e. sqr(5) ) coefficients
if you want "nice" numbers use the roots ½ , 3+ √5 and 3- √5

in other words, multiply out
2(x-½)(x-(3+ √5)) (x+ (3+ √5))