Question

Which of the following is a polynomial with roots 3, 5i, and −5i?

A.) f(x) = x^3 - 3x^2 + 25x - 75
B.) f(x) = x^3 - 3x^2 + 15x - 25
C.) f(x) = x^3 - 15x^2 + 25x - 75
D.) f(x) = x^3 - 3x^2 + 15x - 75

Answer 1

ax^3+bx^2+cx+d has three roots and imagine x,y and z are it's roots. then
x+y+z=-b/a
xyz=-d/a
xy+zx+yz=c/a

Answer 2

the roots are 5i,-5i,3
x+y+z=-b/a
3=-b/a
b/a=-3

xyz=3*25=75=-d/a
d/a=-75
in all of answers a=1so b=-3 and d=-75 so answer is x^3 - 3x^2 + 25x - 75