Solving quadratics using various methods

There are a number of ways to solve quadratics. Remember that when we say solve we are actually finding the $x$x-intercepts or roots of the equation.

We have seen:

• Algebraically Solve - for simple binomial quadratics like $x^2=49$x2=49.
• Factorise - fully factorising a quadratic means we can then use the null factor law: if $a\times b=0$a×b=0 then either $a=0$a=0 or $b=0$b=0.
• Completing the square - this method gets us to a point where we can then solve algebraically. It also tells us the vertex of the quadratic.
• Quadratic Formula - this method will solve any quadratic function of the form $ax^2+bx+c=0$ax2+bx+c=0, but it is not always the easiest to deal with algebraically, sometimes the other methods are a better choice.

When looking to solve a quadratic, check for easy options:

• Can we remove a common factor immediately? 
• Can we solve it straight away algebraically?
• Can we factorise it easily?

If these first two options haven't worked then we can either complete the square or use the quadratic formula.

Let's have a look at these questions.

Question 1

Question 2

Question 3

Question 4