Solving Quadratic Equations with Factorisation

What is Quadratic Equations?

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0. Quadratic equations can be solved in many ways, such as factorisation and completing the square.

What is Factorisation?

Factorisation is a process of breaking down an expression into factors that can be multiplied together to give the original number or expression. It is often used to solve quadratic equations, as it can help to simplify the equation and make it easier to solve.

How to Factorise x3+13×2+32x+20?

To factorise the equation x3+13×2+32x+20, we first need to rearrange the terms into a standard form. The standard form for a quadratic equation is ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0. In this case, the equation is already in standard form, with a = 1, b = 13 and c = 20.

Step 1: Find two numbers that multiply to give c and add to give b.

In this case, c is 20, so we need to find two numbers that multiply to give 20 and add to give 13. The two numbers are 4 and 5, as 4 x 5 = 20 and 4 + 5 = 9.

Step 2: Rewrite the equation in the form (x + a)(x + b) = 0.

We can now rewrite the equation in the form (x + 4)(x + 5) = 0, where a = 4 and b = 5.

Step 3: Factorise the equation.

The equation can now be factorised to give (x + 4)(x + 5) = 0. This means that the equation has two solutions, x = -4 and x = -5.

Conclusion

Factorisation is a useful technique for solving quadratic equations. It can help to simplify the equation and make it easier to solve. In this article, we looked at how to factorise the equation x3+13×2+32x+20 and found that its two solutions are x = -4 and x = -5.