This method of solving quadratic equations may be familiar to you. Recall that before trying to solve any quadratic equation, we must put it in
standard form:ax2 + bx + c = 0
Once the equation is in standard form try to factor it. If you are unsure about factoring, review the
Factoring Notes. After factoring, we will apply the zero product property.The Zero Product Property
If AB = 0, then A = 0 or B = 0. Meaning that if we multiply two things together and get 0, one of them must be 0.
To apply the zero product property, we set each factor equal to zero and solve for the variable.
Here is an example: x2 - 2x - 15 = 0
Since the equation is already in standard form, the first step is to factor:
(x - 5)(x + 3) = 0
Now apply the zero product property. Setting x - 5 = 0 and x + 3 = 0 produces the answers x = 5 and x = -3.
Solve each of the following by factoring and using the zero product property.
1. 4x2 - 25 = 0 Solution
2. 6x2 = 43x + 40
Solution3. 3x2 - x - 14 = 0
Solution
#1 solution
4x2 - 25 = 0
Since the equation is already in standard form, the first step is to factor. Note that we have a
difference of squares:(2x - 5)(2x + 5) = 0
Now apply the zero product property and set each of the factors equal to zero.
2x - 5 = 0 or 2x + 5 = 0
We now have two linear equations to solve.
#2 solution
6x2 = 43x + 40
Since the equation is
not in standard form, the first step is to put it in standard form. Subtract 43x and 40 from both sides of this equation. Doing this, we get:6x2 - 43x - 40 = 0
Now that the equation is in standard form, factor the trinomial.
(6x + 5)(x - 8) = 0
Next apply the zero product property and set each of the factors equal to zero.
6x + 5 = 0 or x - 8 = 0
We now have two linear equations to solve.
6x = -5 or x = 8
x = -5/6 or x = 8
#3 solution
3x2 - x - 14 = 0
Since the equation is in standard form, we will factor the trinomial.
(3x - 7)(x + 2) = 0
Next apply the zero product property and solve.
3x - 7 = 0 x + 2 = 0
3x = 7 x= -2
x = 7/3