Find a cubic equation with integral coefficients that has the given roots.
4+i sqrt3 all over 2 and -1
if 4 + i√3 over 2 is a root, so is 4 - i√3 over 2
The sum of these is 8/2 = 16/4
the product is 16 - i^2 (3) over 4 = (16 + 3) / 4 = 19/4
so the quadratic giving those roots is (4x² - 16x + 19)
[since the sum of the roots of ax^2 + bx + c is -b/a, and the product is c/a]
and the -1 comes from a factor of (x + 1)
so multiply (x + 1)(4x² - 16x + 19)
im in 8th grade algebra so im no help
Comments
if 4 + i√3 over 2 is a root, so is 4 - i√3 over 2
The sum of these is 8/2 = 16/4
the product is 16 - i^2 (3) over 4 = (16 + 3) / 4 = 19/4
so the quadratic giving those roots is (4x² - 16x + 19)
[since the sum of the roots of ax^2 + bx + c is -b/a, and the product is c/a]
and the -1 comes from a factor of (x + 1)
so multiply (x + 1)(4x² - 16x + 19)
im in 8th grade algebra so im no help