Find all roots rational irrational and or imaginary given the first one or two

Question

X⁴ -5x²-36=0 ;roots +-3

Answer 1

Begin by using synthetic division with the first two roots. It should look like this

3 1 0 -5 0 -36

3 9 12 36

-3 1 3 4 12 0 <--- Remainder, Now use this cubic with the second root

-3 0 -12

1 0 4 0 <------Remainder, this gives you a quadratic that can be solved using the sqrt prop.

x² + 4 =0

x² = -4 take the sqrt of both sides

x = 4 i , -4 i

Patti D.