can someone help me with Nature of roots and zeros?
Find all the zeros of each polynomial function.

f(x) = x4 – 5x2 – 36

1) Select one:
a. ±3, ±2i
b. ±3 only
c. ±2i only
d. none of the above

Question

can someone help me with Nature of roots and zeros? 
Find all the zeros of each polynomial function.
 
f(x) = x4 – 5x2 – 36

1) Select one:
a. ±3, ±2i 
b. ±3 only 
c. ±2i only 
d. none of the above

anonymous · Answer

To find the roots of a polynomial equation you should:


Select one:
a. only use Descartes Rule of Signs. 
b. only use the Quadratic Formula. 
c. only factor it. 
d. use any method that gives the roots of the function.

barrycarter · Answer

Hint (for original problem): substitute y = x^2

anonymous · Answer

huh?

campbell_st · Answer

what has been suggested is that this equation is reducible to a quadratic equation... 

this can be done by using an appropriate substitution... such as letting y = x^2

so the equation becomes 

$$y^2 - 5y - 36 $$

now you can use the general quadratic formula  

$$y = \frac{5 \pm \sqrt{25 - 144}}{2}$$

then when you get the values for y, replace it with x^2 and then solve for x