Find zeroes of the polynomial

Let a, b, c be the zeroes of the given polynomial such that a + b = 0 (since two zeroes are equal in magnitude but opposite in sign)

Now, using the relation between coefficients and zeroes, We have:

Sum of zeroes = -(-5)/1 = 5 = a+b+c

This gives c = 5

 

Also, product of zeroes = -80/1

This gives 5ab = -80

ab = -16

-a² = -16   (Since, a+b=0 => b = -a)

So, a = 4, or -4

Now, when a = 4, b = -4

and when a = -4, b = 4

 

Thus, the roots are 4, -4, 5.