Question

4) x2 - 2x + 2 = 0

4. 1)

a

4. 2) What is the exact value of the DISCRIMINANT? b2 - 4ac -

*Type this into your calculator

O2 - 400

4. 3) Which type of SOLUTIONS does this parabola have ? =

(REAL or IMAGINARY)

4. 4) Why? (* Remember to think about the SQUARE ROOT symbol * ) =

Answer 1

See below

Explanation:

Solve the equation using the quadratic formula

`\displaystyle x^2-2x+2=0\\\\x=(-b\pm√(b^2-4ac))/(2a)\\\\x=(-(-2)\pm√((-2)^2-4(1)(2)))/(2(1))\\ \\x=(2\pm√(4-8))/(2)\\ \\x=(2\pm√(-4))/(2)\\ \\x=(2\pm2i)/(2)\\ \\x=1\pm i`

Discriminant and Solution Analysis

As we determined in the quadratic formula, our discriminant is -4 because
`b^2-4ac=(-2)^2-4(1)(2)=-4`, under the radical. Because it is negative, our solutions must be imaginary since the square root of a negative number is not real.