Vivekanand Vellanki
1

The zero product property states that if ab = 0, then one of the following must be true: a = 0, or b = 0, or a = b = 0.


In this case, you need to factorise the equation 4x^2 - 4x - 3 = 0 so that it looks like ab = 0.


For an equation of the form: ax^2 + bx + c = 0, the steps to factorise the equation are:

  1. Find 2 numbers, p and q, such that
  2. pq = ac, and p+q=b
  3. Then, you can factorise the equation as \frac{1}{a\ }\left(ax+p\right)\left(ax+q\right)=0


For this equation, you need to find two numbers p and q such that:

pq = -12 (4*-3) and

p+q = -4


Look at the factors of -12 and see if you find any that add up to -4.