Quadratic Equations are equations of the form ax^2 + bx + c = 0 where , and are real numbers and . Depending on the form of the equation, you can solve for by extracting the quare root, factoring, or using the quadratic formula.This type of equation appears in various problems that involves multiplication and usually appears in the Civil Service Exams.
The following series details the method and strategies in solving problems involving quadratic equations.
In the previous two posts (Part 1 and Part 2), we have discussed two problems involving quadratic equations. The first one is
A rectangular flower garden with dimensions 3m by 7m is surrounded by a walk of uniform width. If the area of the walk is 11 square meters, what is the width of the walk in meters?
If we let be the width of the walk, then the length of the walk becomes and the width becomes as shown in the figure below.
We know that the area of the garden (the inner rectangle) is equal square meters. The area of the larger rectangle is equal to
Now, to get the area of the walk, we have to subtract the area of the garden from the area of the large rectangle. That is,
area of the larger rectangle – area of the smaller rectangle = 11
Subtracting 11 from both sides, we have
Now, the quadratic equation is not factorable, so we use the quadratic formula in order to find the value of x. In using the quadratic formula, we want to identify the values of a, b, and c in the equation and substitute in the quadratic formula
From the equation above, , and . Substituting these values in the quadratic formula, we have
That means that we have two roots
As we can see, we is not a possible root because it is negative. Therefore, the acceptable answer to the problem is
This means that the width of the walk is ½ meters.
Check: If the width of the walk is ½ meters, then the length of the larger rectangle is and the width is . The area is sq. m.
Now the area of the walk is meters and sq. m. which is the area of the walk indicated in the problem. Therefore, we are correct.
You can also watch the Youtube video below regarding the discussion above.