Question

factorise x^2-x+4=0​

Answer 1

Answer:

So equation can be written in the form of (x+a)*(x+b)

Where (x+a),(x+b) are factors of the equation.

So by expanding we get x^2+(a+b)x+ab.

By comparing the above equation with the given equation we get a+b=-1, ab= 4

We know that (a-b)^2=(a+b)^2–4ab

So we get (a-b)^2=(-1)^2–4(4)

(a-b)^2=1–16

(a-b)^2=-15

(a-b)=√-15

So a-b=+√15i or -√15i

So a+b=-1 and let a-b=√15i

Adding both equations we get 2a=-1+√15i

So a=(-1+√15i)/2 and substituting a in the above one of the equation we get b=(-1–√15i)/2

Similarly by taking a-b=-√15i we get

a=(-1-√15i)/2 and b=(-1+√15i)/2

So the factors of the given equation are

(x+(-1+√15i)/2) and (x+(-1-√15i)/2)

thank you for a wonderful question