Factorise: x squared - 2x + c?

Question

In the form (x +/- a)(x +/- b) stating the value of a, b and c, where c is an integer.

Answer 1

I just used the quadratic formula and found that the roots are 1 +/- sqrt(1-c). That means the factors are (x - a) and (x - b), where a and b are the two roots. The roots have real values when c <= 1, and complex values when c > 1.

The quadratic formula, in case you don't know it, is (-b +/- sqrt(b^2 - 4ac))/2a, where the expression written as ax^2 + bx + c. In your expression, a = 1, b = -2, and c = c. Try not to be confused by the fact that both expressions use a, b, and c.

Answer 2

The roots can be obtained by using the formula
{-b +/- sqrt(b^2-4ac)}/ 2a

= {2 +/- sqrt(4-4c)}/2
= 1 +/- sqrt(4-4c)/2
= 1 +/- sqrt(1-c) ; c<=1
=> {x - 1 - sqrt(1-c)} {x - 1 + sqrt(1-c)}

Answer 3

x^2-2x + c
= x^2-2x +1 + c-1(add 1 to make it whole square)
=(x-1)^2 -(1-c)
=(x-1)^2 - sqrt(1-c)^2 (to get in form a^2-b^2)
= (x-1+sqrt(1-c))(x-1-sqrt(1-c))

Answer 4

For this you need to use the quadratic formula which I suggest you look up as writing it out here would be baffling.