SOLUTION: Use the given zero, 5i, to find all the zeros of the function: f(x)=2x^3+3x^2+50x+75

Algebra ->  Trigonometry-basics -> SOLUTION: Use the given zero, 5i, to find all the zeros of the function: f(x)=2x^3+3x^2+50x+75      Log On


   

Question 626148: Use the given zero, 5i, to find all the zeros of the function: f(x)=2x^3+3x^2+50x+75
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The complex zeros always come in pairs that
look like +a+%2B+b%2Ai+ and +a+-+b%2Ai+, so the
pairs of factors are +x+-+5%2Ai+ and +x+%2B+5%2Ai+
If I multiply these, I get +x%5E2+-+25%2A%28-1%29+=+x%5E2+%2B+25+
------------
Now I divide +2x%5E3+%2B+3x%5E2+%2B+50x+%2B+75+
by +x%5E2+%2B+25+ and I get +2x+%2B+3+ as the
3rd factor . Set it equal to zero.
+2x+%2B+3+=+0+
+2x+=+-3+
+x+=+-%283%2F2%29+
Here's the plot:
+graph%28+500%2C+500%2C+-10%2C+10%2C+-200%2C+200%2C+2x%5E3+%2B+3x%5E2+%2B+50x+%2B+75+%29+