How do I find zeroes of quadratic functions?

To find the zeros of the quadratic equation, you have to find out the values of the unknwons for which the quadratic expression becomes zero. The quadratic equation is an equation of second degree equation of an unknown (or  variable ).

Examples:

1) x^2 = 9. Solution: x = + (9)^(1/2) = 3 or x = -(9)^(1/2) =-3

Second way: x^2=9 . Subtract 9 from both sides. Then x^2-9= 0 . Factorising the left you get:(x-3)(x+3) = 0. To get zero of the product, one of the products, x-3 =0 or x+3 = 0 which gives you the zeros of the equation, x^2 = 9 or x^2 - 9 = 0 to be x=3 or x = - 3.

2) 5x^2 = 14: Solution  x^2 =  14/5. So x= -or+ [sqrt(14/5)]

3) Now you can generalise the procedure. But I give you a numerical  type example of the type ax^2+bx+c = 0 form.

x^2-3x+2=0 could be re written like:

x^2-3x+(3/2)^2-(3/2)^2+2 =0, adding subtracting (3/2)^2 to make it perfect square and number .

(x-3/2)^2 -(3/2)^2+2 = 0

(x-3/2)^2 = (3/2)^2- 2 =  9/2 - 2 =1/4

Taking square root,

x-3/2 = + or-1 sqrt(1/4) = +or (1/2)

x = 3/2+1/2 = 2 or x= 3/2-1/2 =1.