Roots of a Quadratic Equation

Another solution to finding the roots of the quadratic above is to factorise the equation and then solve.

So if we are looking at the above where x2-3x-4.

What 2 numbers multiply together to equal -4 but also add together to equal -3.

So let’s look at the multiplication first:

For -4 we could have the following.

1 x -4

-1 x 4

-2 x 2

2 x -2

Now let’s add each of these.

1 + (-4) =-3

-1 + 4 =3

-2 + 2 =0

2 + -2 =0

which of the above equals -3

1 and -4 these must be our factors

so we have (x + 1)(x - 4)

what would x have to equal to make each bracket total 0

so what + 1 = 0 … -1 great

and same for the other = 4

so our values for x are -1 and 4

1. At x=−1x = -1x=−1:
2. (−1)2−3(−1)−4=1+3−4=0(-1)^2 - 3(-1) - 4 = 1 + 3 - 4 = 0(−1)2−3(−1)−4=1+3−4=0 ✅
3. At x=4x = 4x=4:
4. 42−3(4)−4=16−12−4=04^2 - 3(4) - 4 = 16 - 12 - 4 = 042−3(4)−4=16−12−4=0 ✅

These roots, x=−1x = -1x=−1 and x=4x = 4x=4, are the solutions of the quadratic equation.

complete the square