Question

Find zeros of the polynomial 5 x square -3 x -2

Answer 1

f(x)=5x -3x- 2 
f(1)=5-3-2=0
hence x-1 is a factor of the polynomial f(x)

now divide f(x) by (x-1)
we get 5x+2
hence 5x+2 is another factor of the polynomial f(x)
5x+2=0
⇒5x=-2
⇒x=-2/5

Hence 1 and -2/5 are the zeroes of the polynomial f(x)
comment if u have doubts

Answer 2

f(x) = 5x sq.-3x-2
  by using the middle term splitting method
     =5xsq.-5x+2x-2
     =5x(x-1)+2(x-1)
     =(5x+2)(x-1)
mow putting both value =0
5x+2=0                  x-1=0
5x=-2                     x=-1
x=-2/5                   beta=-1 
alpha =-2/5

so two zeroes are -2/5 and -1