This post is about factoring a quadratic equation without the middle term. In order to read the post about factoring a quadratic equation by splitting the middle term, go here:
Factoring quadratic equations without a middle term (pure quadratic equations)
Method 1
It is very simple to factor a quadratic equation without a middle term (a pure quadratic equation).
For example, we will factor the equation
(learn more about why there are two square roots of a positive number)
Thus it is only a matter of finding the square root when you have to solve a quadratic equation without the middle term.
Method 2
The second method involved algebra. It is based on the algebraic difference between two squares. The particular formula used here is
Factoring a quadratic equation by splitting the middle termIn order to read the post on factoring a quadratic equation by the box method, go here:
Factoring by box methodA quadratic equation without b, or the middle term, is known as a pure quadratic equation. Examples of such equations are:
- `x^2 - 9 = 0`
- `x^2 + 23 = 27`
- `x^2 = 100`
Factoring quadratic equations without a middle term (pure quadratic equations)
Method 1
It is very simple to factor a quadratic equation without a middle term (a pure quadratic equation).
For example, we will factor the equation
`x^2 - 9 = 0`Step 1: Move the number -9 to the other side. To do this, we will add 9 to both sides (since it is negative on the LHS)
`x^2 = 9`Step 2: Now take square root of both sides, so we obtain
`x = +/- sqrt(9)`Hence the answer is `x = +3` or `x = -3`, because both +3 and -3 are square roots of 9.
(learn more about why there are two square roots of a positive number)
Thus it is only a matter of finding the square root when you have to solve a quadratic equation without the middle term.
Method 2
The second method involved algebra. It is based on the algebraic difference between two squares. The particular formula used here is
`a^2 - b^2 = (a + b)(a - b)`We will consider a pure quadratic equation as a difference of two squares. For example, the equation
`x^2 - 9 = 0`can be written as a difference of two squares as follows:
`x^2 - 3^2 = 0`Now applying the property `a^2 - b^2 = (a + b)(a - b)`, we get
`(x + 3)(x - 3) = 0`Now applying the zero product rule, we get
Either x = -3 or x = 3Thus a quadratic equation/function that does not have a pure quadratic equations can be solved by two methods. The method 1 described above will be able to quickly solve all such quadratic equations.
