So far, we have studied the four methods to solve a quadratic equation. How do we select the best method to solve among these four methods?
The following table will guide us to choose the best method to solve.
Method | When to choose |
Use if we need only the appropriate solutions. However, we can use it always. | |
Use if we could easily determine the factors or the constant term is zero. | |
Use if the equation is of the form x2 + bx + c = 0 and b is even. However, we can use it always. | |
We can use this method to any type of quadratic equation. In some cases, the other methods will be easy to solve. |
Example:
The product of two consecutive positive odd integers is 99. Find those two numbers.
Solution:
Step 1:
Given that the product of two consecutive positive odd integers is 99.
We are asked to find the two consecutive positive odd integers.
Let the first integer be x.
Then the consecutive positive odd integer is x + 2.
Given that the product of x and x + 2 = 99
=> x(x + 2) = 99
=> x2 + 2x - 99 = 0
So, we arrived at a quadratic equation x2 + 2x - 99 = 0.
Step 2:
We can solve the quadratic equation by using factoring.
x2 + 11x - 9x - 99 = 0
=> x(x + 11) - 9(x + 11) = 0
=> (x + 11)(x - 9) = 0
=> x + 11 = 0 or x - 9 = 0
=> x = -11 or x = 9
Step 3:
Since we are looking for a positive number, neglect -11.
So, x = 9.
If x = 9, then x + 2 = 9 + 2 = 11.
Step 4:
Hence, the two consecutive positive odd numbers are 9 and 11.
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