Question

Find the zeroes of x 3 -5x ​2 -16x+80,if its 2 zeroes are equal in magnitude but opposite in sign.

Answer 1

Equation is x³ -5x² -16x +80=0
Let the roots be b,a and -a
sum of roots,
(b+a-a) = 5
⇒b = 5
means, one root is 5

i.e.(x-5 ) is a factor of x³ -5x² -16x +80=0

x-5) x³ -5x² -16x +80( x²-16
       x³-5x²
     -    +
      0   0   -16x+80
                -16x+80
                +     -
                  0     0

So, the other factor will be (x²-16)
so, (x²-16) =0
⇒x = 4 and -4

∴Zeroes will be 5, 4 and -4