Question

Factor the following trinomials.
x²-6x+4

Answer 1

`(x-3-√(5))(x-3+√(5))`

Explanation:

Start with the discriminant of the trinomial

`x^2-6x+4`

The discriminant is

`D=b^2-4ac=(-6)^2-4\cdot 1\cdot 4=36-16=20`

Now, find the roots of the trinomial using the quadratic formula

`x_(1,2)=(-b\pm √(D))/(2a)=(-(-6)\pm √(20))/(2\cdot 1)=(6\pm2√(5))/(2)=3\pm √(5)`

So, the factored form of the trinomial is

`(x-(3+√(5)))(x-(3-√(5)))=(x-3-√(5))(x-3+√(5))`