Question

Write a polynomial function of least degree with integral coefficients that has the given zeros.

1. -3 + √10, -3 - √10, √5

Answer 1

degree 4 with Integer ?

Answer 2

you remember the zeros of a polynomial are the solutions of

y = P(x) = 0

Answer 3

and when you factored sometimes, you had a product of quantities , if any one was 0, then y=0

( x + )(x + ).....=0

Answer 4

oh so is it (+3-√10) ?

Answer 5

this is the reverse, make quantities using each of those given zeroes,

\[(x - 1)*(x - \sqrt{5}) = 0\]

that takes care of 2 of the 4,

Answer 6

when x=1, you get p(x)=0 , also when x is root5,

Answer 7

if those are complex number pair, is there an imaginary i in them , or they just real numbers like that

Answer 8

\[(x - 1)*(x - \sqrt{5})*(x + (-3 + \sqrt{10})*(x + (-3 - \sqrt{10})) = 0\]

that there works for all them zero values given for x.

you just need to expand all that out into standard polynomial , most likely

Answer 9

ohhh okay, i see now thanks!

Answer 10

welcome