Question

Which expression is equivelent to x^2 +2x+2

Answer 1

(x+1-i)(x+1+i)

Explanation:

`\dashrightarrow \: { \tt{ {x}^(2) + 2x + 2 }}`

• From the general quadratic equation:

`\dashrightarrow \:{ \boxed { \tt{ {ax}^(2) + bx + c }}}`

• Sum = (b/a)
• Product = (c/a)

From x² + 2x + 2:

• Sum = 2
• Product = 2
• Factors = No real roots

From Bulldozer;

`{ \tt{x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a} }} \\ \\ { \tt{x = ( - 2 \pm √(4 - (4 * 1 * 2)) )/(2) }} \\ \\ { \tt{x = ( - 2 \pm √( - 4) )/(2) }} \\ \\ { \tt{x = \frac{ - 2 \pm \sqrt{4 {i}^(2) } }{2} } \: \: \{ \red{for \: - 1 = {i}^(2) } \}} \\ \\ { \tt{x = ( - 2 \pm2i)/(2) }} \\ \\ { \tt{x = - 1 \pm i}}`

Therefore;

`{ \tt{(x + 1 + i)(x + 1 - i)}}`