Solving Quadratic Equations Using Factorisation A quadratic equation in the form of $$ax^2 + bx + c = 0$$ is a mathematical equation where $$a, b, \text{ and...
A quadratic equation in the form of is a mathematical equation where are constants. Solving a quadratic equation involves finding the roots of the equation, which are the values of that make the equation equal to zero.
Factorisation is a method for factoring a quadratic equation into two linear factors. A quadratic equation can be factored into two linear factors in the form of
How to factorise a quadratic equation:
Identify the coefficients of the quadratic equation. The coefficients are the values of a, b, and c.
Factor the left-hand side of the equation. This means finding two numbers that multiply to the coefficient of the term and add up to the coefficient of the term.
Match the factors to the linear factors. The factors should be the same as the linear factors in the factored equation.
Combine the linear factors into a factored equation. Add the coefficients of the terms together to get the coefficients of the squared term, and the constant term to form the constant of the factored quadratic equation.
Example:
Solve the quadratic equation
Step 1: Identify the coefficients: a = 1, b = 6, and c = 9.
Step 2: Factor the left-hand side:
Step 3: Match the factors to the linear factors:
Therefore, the solutions are x = -3 and x = -3.