A quadratic equation is an important topic in Class 10 Maths. It is an equation in which the highest power of the variable is 2. Learning how to solve quadratic equations becomes easy when we follow the steps carefully.
In simple words, a quadratic equation usually looks like this:
ax² + bx + c = 0
Here, a, b, and c are numbers, and a is not zero.
How to Solve a Quadratic Equation?
There are different methods for solving quadratic equations. The common methods are factorisation, completing the square, and the quadratic formula.
First, let us understand the factorisation method with an easy example.
Example: Solve x² − 5x + 6 = 0
Step 1: Write the equation
x² − 5x + 6 = 0
Step 2: Find two numbers
We need two numbers whose product is 6 and whose sum is −5.
The numbers are −2 and −3.
Step 3: Factorise the equation
x² − 5x + 6 = 0
So,
(x − 2)(x − 3) = 0
Step 4: Find the values of x
If:
x − 2 = 0
then:
x = 2
Also, if:
x − 3 = 0
then:
x = 3
Therefore, the two roots or solutions are:
x = 2 and x = 3
Quadratic Formula
Sometimes a quadratic equation cannot be easily factorised. In that case, we can use the quadratic formula.
For:
ax² + bx + c = 0
the formula is:
x = (−b ± √(b² − 4ac)) / 2a
This formula can be used to find the roots of a quadratic equation.
For example, in 2x² + 3x − 2 = 0, we have:
- a = 2
- b = 3
- c = −2
Put these values into the formula and simplify to find the two answers.
Why Are Quadratic Equations Important?
Quadratic equations are useful in many Class 10 Mathematics problems. They help students understand algebra and solve problems involving numbers, shapes, and real-life situations.
Quick Revision
Remember these simple points:
- A quadratic equation has the highest power 2.
- It can have two roots.
- Factorisation is useful when the equation can be easily broken into factors.
- The quadratic formula can be used when factorisation is difficult.
- Always check your answer by putting the value of x back into the original equation.
With regular practice, solving Class 10 quadratic equations becomes much easier.