Question

find the zeros of the quadratic polynomial 9x^2-1 and verify the relationship between the zeros and coefficients.

Answer 1

$9 x^{2} -1=0 \\ (3x)^{2} - 1^{2} =0 \\ (3x-1)(3x+1)=0$
then,
         (3x-1) = 0
  so,   x = 1/3
and (3x+1) = 0
  so,  x = -1/3
we can verify this result by put the value of x in equation

Answer 2

9x^2-1=0
adding 1 on both sides
9x^2-1+1=0+1
9x^2=1
dividing both sides by 9
9x^2/9=1/9
x^2=1/9
x=plur or minus 1/√9
x=plus or minus 1/3