Determine if the complex number, 2+ i, is a solution to the quadratic equation 3x2 - 6x + 6 = 0

Explain your answer.

Question

Determine if the complex number, 2+ i, is a solution to the quadratic equation 3x2 - 6x + 6 = 0


Explain your answer.

misty1212 · Answer

hi
easiest just to solve if and see what you get

misty1212 · Answer

$$3x^2-6x+6=0$$ divide by 3 and solve 
$$x^2-2x+2=0$$ 
you know how to solve this one?

anonymous · Answer

Plug in 2 + i to your equation

misty1212 · Answer

probably easiest in this case to complete  the square because 2 is even
 it will be real annoying to try to evaluate it at $x=2+i$

misty1212 · Answer

the answer will probably be no in any case

anonymous · Answer

Can you please explain why it is not a solution

misty1212 · Answer

sure 
when we solve it we will get something else!

anonymous · Answer

Okay thank you . Could you help me with one more?

misty1212 · Answer

$$x^2-2x+2=0\
x^2-2x=-2\
(x-1)^2=-2+1=-1\
x-1=\pm i\
x=1\pm i$$

misty1212 · Answer

the solutions are $1\pm i$ not $2\pm i$

misty1212 · Answer

sure why not?

anonymous · Answer

Determine if 1 - i is a solution to the equation 2x2 - 4x + 4 = 0. 


Explain your answer.

misty1212 · Answer

lol this is really sooo much different than the last one
why don't they just ask you to solve it instead of screwing around with "is blah blah..."

misty1212 · Answer

$$2x^2-4x+4=0$$ divide by 2
$$x^2-2x+2=0$$ subtract 2
$$x^2-2x=-2$$ complete the square 
$$(x-1)^2=-2+1=-1$$ take the square root 
$$x-1=\pm i$$ solve for $x$$$x=1\pm i$$

misty1212 · Answer

so this time the answer is YES

anonymous · Answer

Thank you so much!

misty1212 · Answer

you are welcome dear glad to help!