Question

Please solve the following quadratic equation and show your work: x^2-2x+6=0

Answer 1

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ exist\ two\ solutions\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta =0\ then\ exist\ one\ solution\ x_o=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solutions$

We have:

$x^2-2x+6=0\\\\a=1;\ b=-2;\ c=6\\\\\Delta=(-2)^2-4\cdot1\cdot6=4-24=-20 < 0$

Answer: NO SOLUTIONS.