CBSE Class 10 Mathematics Chapter 4 - Quadratic Equations - Solution of a Quadratic Equation by Factorisation

CBSE Class 10 Mathematics  Chapter 4 - Quadratic Equations - Solution of a Quadratic Equation by Factorisation

Solution of a Quadratic Equation by Factorisation

Step 1: Write the Quadratic Equation in Standard Form

• Make sure the equation is in the standard form: ax² + bx + c = 0, where a, b and c are constants and a ≠ 0.

Step 2: Factor the Quadratic Expression

Factor the quadratic expression on the left side of the equation. This involves finding two binomials (expressions with two terms) that, when multiplied must be equal the quadratic expression. For example:

ax² + bx + c = 0

Factor the quadratic expression into two binomials:

(ax + m)(x + n) = 0

Where 'm' and 'n' are constants that we need to determine.

Step 3: Set Each Binomial Equal to Zero

Set each binomial equal to zero and solve for 'x':

ax + m = 0

Solve for 'x' by isolating it on one side:

ax = -m

x = — m/a

x + n = 0

Solve for 'x' by isolating it on one side:

x = —n

Step 4: Solve for 'x'

We now have two equations for 'x':

x = — m/a

x = — n

Step 5: Determine the Values of 'x'

Solve for 'x' by substituting the values of ‘m’, ‘n’, and ‘a’ that we found while factoring the quadratic expression. This will give us the solutions to the quadratic equation.

Step 6: Check for Validity

It's important to check the validity of the solutions by plugging them back into the original quadratic equation. If both solutions make the equation true, they are valid solutions.

Step 7: Write the Solutions

Write the solutions for 'x' as ordered pairs if the solutions are real numbers.

Note: Keep in mind that not all quadratic equations can be easily factored and this method may not work for all cases. In such situations, you may need to use the quadratic formula or other methods to find the solutions.