Question

Splitting middle term x²-5x+16​

Answer 1

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=5, ab=16

We know that (a-b)^2=(a+b)^2–4ab

So we get (a-b)^2=(5)^2–4(6)

(a-b)^2=25–24

(a-b)^2=1

(a-b)=+1 or -1

So a-b=+1 or -1

So a+b=5 and let a-b=1

Adding both equations we get 2a=16

So a=3 and substituting a in the above one of the equation we get b=2

Similarly by taking a-b=-1we get

a=2 and b=3

So the factors of the given equation are

(x+2) and (x+3)..