How do you factor $x^{2} - 2 x + 2$ $x^2-2x+2$ ?

Responda:

This quadratic only factors with the help of Complex coefficients:

$x^{2} - 2 x + 2 = (x - 1 - i) (x - 1 + i)$ $x^2-2x+2 = (x-1-i)(x-1+i)$

Explicação:

Dado:

$x^{2} - 2 x + 2$ $x^2-2x+2$

Isto está na forma $a x^{2} + b x + c$ $ax^2+bx+c$ com $a = 1$ $a=1$ , $b = - 2$ $b=-2$ e $c = 2$ $c=2$

It has discriminant $Delta$ given by the formula:

$Delta = b^2-4ac = (color(blue)(-2))^2-4(color(blue)(1))(color(blue)(2)) = 4 - 8 = -4$

Desde $Delta < 0$ , this quadratic has no Real zeros and no linear factors with Real coefficients.

We can still factor it, but we need to use Complex coefficients.

A diferença da identidade dos quadrados pode ser escrita:

$A^2-B^2 = (A-B)(A+B)$

To factor our quadratic, we can complete the square and use the difference of squares identity with $A=(x-1)$ e $B=i$ como se segue:

$x^2-2x+2 = x^2-2x+1+1$

$color(white)(x^2-2x+2) = (x-1)^2+1$

$color(white)(x^2-2x+2) = (x-1)^2-i^2$

$color(white)(x^2-2x+2) = ((x-1)-i)((x-1)+i)$

$color(white)(x^2-2x+2) = (x-1-i)(x-1+i)$

How do you factor x^2-2x+2x2−2x+2 x^2-2x+2 ?

Responda:

Explicação:

How do you factor $x^{2} - 2 x + 2$ $x^2-2x+2$ ?