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Representing real-life situations as quadratic equations

This means turning a word problem or geometry problem into a quadratic equation by choosing a variable and forming the correct relation.

In one line: Words first, equation second, answer last.

Practice This Concept

Understand it

Many CBSE questions describe lengths, areas, products, or consecutive numbers in words. The student must translate the words into an equation, rearrange it into standard form, and then solve it.

Example

If breadth is x and length is x + 5, then area 84 gives x(x + 5) = 84.

Formula and rule

Use area = length × breadth, product relations, or consecutive-number relations like x(x + 1) or x(x + 2) when the question describes real situations.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A rectangle has breadth x cm and length x + 5 cm.

1Its area is 84 cm².
2So x(x + 5) = 84.
3Expanding gives x² + 5x - 84 = 0, which is the quadratic equation to solve.

Method you can reuse

1Read the relation carefully.
2Let the unknown quantity be x.
3Write the formula from the context.
4Expand the expression.
5Rearrange it into ax² + bx + c = 0.
6Solve using the suitable method.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does a rectangle problem often lead to a quadratic equation?

Think first, then show answer

Because area is found by multiplying two expressions, such as x and x + 5. After expansion, the relation usually becomes a degree-2 equation, which is quadratic.

Common wrong answer

Writing x² + 5x = 84 and stopping there is incomplete because the equation is not yet in standard form.

Don't mix this up

Students often write the relation correctly but forget to bring all terms to one side before solving.

Exam tip

Choose one variable clearly, build the relation from the question, and expand carefully before solving.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

The exam may present a practical situation and ask for the equation first, then the value of x and the final dimensions.

1
Enough for 1 mark
This means turning a word problem or geometry problem into a quadratic equation by choosing a variable and forming the correct relation.
2
Add for 2 marks
Example: If breadth is x and length is x + 5, then area 84 gives x(x + 5) = 84.
3
Add for 3 marks
A rectangle has breadth x cm and length x + 5 cm.

MCQ Quiz

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