SOLUTION: Hi tutor ! So im a 14 year old who lives in texas . Ive really been struggling with the quadratic formula and would love for you to help me where i need help . Please please please

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi tutor ! So im a 14 year old who lives in texas . Ive really been struggling with the quadratic formula and would love for you to help me where i need help . Please please please      Log On


   

Question 962773: Hi tutor ! So im a 14 year old who lives in texas . Ive really been struggling with the quadratic formula and would love for you to help me where i need help . Please please please respond here , on my email , or through text 2144317404 ! Thank you and God bless you .
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic formula is about a "general"
quadratic equation, namely:
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
Then you set +f%28x%29+=+0+ to find the "roots"'
which are the solutions
+a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0+
------------------------
Suppose your equation for finding roots looks like:
+-4x%5E2+%2B+6x+-+11+=+0+
Then, comparing to the "general" equation:
+a+=+-4+
+b+=+6+
+c+=+-11+
----------------
Now you have to plug these values into the "general"
formula for finding the roots:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
The tricky thing about this formula is that it is TWO formulas:
x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
and
x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
-------------------------------------
That's because of the + or - in front of the square root sign
---------------------------
Now plug in values:
x+=+%28-6+%2B-+sqrt%28+6%5E2+-+4%2A%28-4%29%2A%28-11%29+%29%29%2F%282%2A%28-4%29%29+
x+=+%28-6+%2B-+sqrt%28+36+-+176+%29%29%2F%28-8%29+
+x+=+%28+-6+%2B-sqrt%28+-140+%29%29+%2F+%28-8%29+
+x%5B1%5D+=+%28+-6+%2B+11.8322i+%29+%2F+%28-8%29+
+x%5B1%5D+=+3%2F4+-+1.4790i+
That is one complex solution
The other one is:
+x%5B2%5D+=+%28+-6+-+11.8322i+%29+%2F+%28-8%29+
+x%5B2%5D+=+3%2F4+%2B+1.4790i+
---------------------------------
So, you ended up with what they call a pair of
complex conjugate roots. That just means they
look like:
+A+%2B+Bi+ and +A+-+Bi+
-----------------------------
Then there is the whole discussion of the "discriminant"
which is the +b%5E2-4%2Aa%2Ac++ part of the formula
Because this is under the square root sign, the
"discriminant" will tell you whether you have:
(1) one "double" root in the case where:
+b%5E2+=+4a%2Ac+
(2) two rational roots when:
+b%5E2+%3E+4a%2Ac+
(3) that pair of complex conjugate roots where:
+b%5E2+%3C+4a%2Ac+
--------------------------------
The picture of the quadratic ( parabola ) tells you right
away which case you have:
(1) the parabola just touches the x-axis
(2) the parabola crosses the x-axis in 2 places
(3) the parabola never touches the x-axis
---------------------------------------
Here's a plot of the 3 cases of the discriminant:

Hope this helps