Question

X2 - 2x + 2 = 0

solve each equation by graphing. if integral roots cannot be found estimate the roots by stating the consecutive integers between which the Roots lie.​

Answer 1

Explanation:

Let's solve x^2 - 2x + 2 = 0 using "completing the square:"

1. Take the coefficient of x: It is -2.

2. Halve this, obtaining -1.

3. Square this result, obtaining 1.

4. Add 1, and then subtract 1, between -2x + 2:

x^2 - 2x + 1 - 1 + 2 = 0

5. Rewrite x^2 - 2x + 1 + 1 = 0 beginning with the square of a binomial

(x - 1)^2 + 1 = 0, or (x - 1)^2 = -1

6. Take the square root of both sides, obtaining x - 1 = ±i, or x = 1 ±i

7. Write out the roots: they are x = 1 + i and x = 1 - i (two complex, different roots). No real roots, so the last command of this question is irrelevant. The graph never touches the x-axis; the graph is in Quadrants I and II and is that of a parabola that opens up.