Solving a quadratic equation by factorisation method — lesson. Mathematics State Board, Class 10.

PDF chapter test TRY NOW

The solution of the quadratic equation is the value of the variable that makes the equation zero. We can say these solutions as roots or zeroes.

There are three methods to solve quadratic equations.

Factorisation
Completing the square
Quadratic formula

Solve by factorisation method

Let us see the procedure to solve the quadratic equation by the factorisation method.

Step 1: Write the given equation in standard form.

Step 2: Express the middle term as the sum of two terms such that the sum satisfies the middle term, and the product should satisfy the extreme product.

Step 3: Group the expression into two linear factors by taking the common term outside.

Step 4: Now, solve for

$x$ by equating each linear factor to zero. The obtained values of

$x$ are called the roots or zeroes of the equation.

Important!

Generally, we say

$\alpha$ is a root of the quadratic equation

$ax^2 + bx + c = 0$ if

$a \alpha^2 + b \alpha + c = 0$ . So that means

$x = \alpha$ is a solution of the quadratic equation.

Example:

Find the roots of the quadratic equation

$2x^2 + 4 = 9x$ .

Solution:

The given equation is

$2x^2 + 4 = 9x$ .

Let us first write the given equation in standard form.

$2x^2 - 9x + 4 = 0$

Now, split the middle term by the above procedure.

$2x^2 - x - 8x + 4 = 0$

Group the expression into two linear factors by taking the common term outside.

$x(2x - 1) - 4(2x - 1) = 0$

$(2x - 1)(x - 4) = 0$

Now, solve for

$x$ by equating each linear factor to zero.

$2x - 1 = 0$ or

$x - 4 = 0$

$x =$

$\frac{1}{2}$ or

$x = 4$

Therefore, the roots of

$2x^2 + 4 = 9x$ are

$\frac{1}{2}$ and

$4$ .

Important!

Any quadratic equation can have at most two roots.

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

5. Solving a quadratic equation by factorisation method

Theory: