Quadratic Formula Example 3.
f(x) = 2x²-8x+10.
So our a value is 2,
our b value is -8,
and our c value is 10.
So, plugging that into my ...
quadratic formula x would equal
-(-8) plus
or minus square root
of (-8)²
minus 4 times
2 times 10
all over
2 times 2.
Simplifying that negative negative 8 would turn that ...
into a positive 8.
plus or minus
inside of my square root
I have (-8)².
Again those parentheses are very important.
minus 4,
times 2,
times 10, when plugging into the calculator.
Enter.
Gives me a -16.
Over 2 times 2 which is 4.
So x
would equal 8 plus or minus.
Now,
we can take the square root of 16,
and sincewe have a negative is also going to be an imaginary.
So -1 times 16.
So the √(-1) would be i.
The √16
would be 4.
So in my
formula, my simplified,
I would end up with 8 plus or minus
4i.
Over
4.
To simplify we're going to divide by
a common factor, in this case,
four will go into all three of my numbers so I can divide each of those
by 4. Remember you can only ...
simplify if you can divide all three parts there.
So 8 divided by 4 would leave me with 2.
plus or minus 4 divided by 4 with 1i.
And 4 divided by 4 would leave me with one in my ...
denominator, which we do not write.
We do not write numbers like this with (2 ± i) over 1.
We leave that denominator off.
So my exact answers
would be x equals
2 + i,
and x equals 2 - i.
In the case, again since there aren't any ...
radicals, our exact answer and our ...
decimal answer will be the same.
x will equal 2 +i,
and  x will equal 2 - i.
Remember when you write complex numbers the i or the ...
imaginary part always goes at the end.
