Question

How do you make a quadratic equation from a word problem?

Answer 1

Hint: Many word problems Involving unknown quantities can be translated for solving quadratic equations. Here, we will use the method to make a quadratic equation from a word problem. We will also take one example to make the concept much clearer. There are various ways to establish a quadratic equation in one unknown from a given word problem. Students must understand the problem first and write the correct quadratic equation and then only they can start solving.

Complete step-by-step answer:
Most quadratic word problems should seem very familiar, as they are built from the linear problems.
Methods of solving quadratic equations are discussed here in the following steps.
Step I: Denote the unknown quantities by x, y etc.
Step II: Use the conditions of the problem to establish in unknown quantities.
Step III: Use the equations to establish one quadratic equation in one unknown.
Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.
Now we will learn how to frame the equations from word problem:

For example:
The product of two consecutive negative integers is 1122. What are the numbers?
We know that consecutive integers are one unit apart.
Let the two consecutive numbers be n and n+1.
From the equation, the product of n and n+1 is 1122.
\[\therefore n\left( {n\; + {\text{ }}1} \right) = 1122\]
\[ \Rightarrow {n^2}\; + \;n\; = 1122\] which is a quadratic in n variable.
\[ \Rightarrow {n^2}\; + \;n\;-{\text{ }}1122 = 0\]
\[ \Rightarrow \left( {n\; + {\text{ }}34} \right)\left( {n\;-{\text{ }}33} \right) = 0\;\]
Thus, the solutions are n = -34 and n = 33.
Since according to the information in the question, we need a negative value.
So, we will ignore n=33 and take n =-34.
For $ n = -34 $
Then $ n+1 = -34 + 1 = -33$
Hence, the two negative numbers are -33 and -34.

Note: f the highest power of the variable of an equation in one variable is 2, then that equation is called a quadratic equation. The quadratic equation will always have two roots. The nature of roots may be either real or imaginary. A quadratic polynomial, when equated to zero, becomes a quadratic equation. The values of x satisfying the equation are called the roots of the quadratic equation.