Finding the Sum of the Roots.
For us to find the sum, we will use the Quad Formula:
Now we'll add
-b+√b²-4ac
¯¯¯¯¯¯¯¯¯
2a
to
-b-√b²-4ac
¯¯¯¯¯¯¯¯¯¯
2a
2a
to get the formula or equation for the sum of roots. It should look like this:
and we're suppose to do this,
-b+-b + √b²-4ac -√b²-4ac
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
2a
and the answer should be,
-2b
¯¯¯¯¯¯
2a
and because we could simplify this, it should be
-b
¯¯
¯¯
a
This answer is our sum of roots. So if we have 2x²+5x-4=0 and your asked to find the sum of the roots you'll just have to use the equation above to find it.
eg. 2x²+5x-4=0 → a=2, b=5, c=-4
Ok, first part is done now we move to the second part,
Finding the Product of the Roots
Of course, for us to know what the product of the roots is, we will still need to use the Quad Formula:
And because we're looking for the product that means we'll need to multiply this:
-b+√b²-4ac
¯¯¯¯¯¯¯¯¯
¯¯¯¯¯¯¯¯¯
2a
to this:
-b-√b²-4ac
¯¯¯¯¯¯¯¯¯
¯¯¯¯¯¯¯¯¯
2a
It should look like this:
then you should have something like this:
The answer is our product of roots.
And if we are to find the product of roots from the first example. we'll just have to do this:
And if we are to find the product of roots from the first example. we'll just have to do this:
Now the third and final part of what we learned this morning.
Determine the equation for given roots.
We'll just need to remember this equation or formula to find the answer or the equation:
x² - sumx + product = 0
Example. Given the roots of 3 , 9
-first find the sum → 3 + 9 = 12
-then find the product → 3 x 9 = 27
-now that we know the sum and the product well just have to replace it with in the equation:
x² - sumx + product = 0 → x² - 9x + 27 = 0
that was pretty easy eh? lol
ooh yeah..
*from the equation ax² - bx + c = 0. These the quad form we usually use.
a, b, and c should be integer coeffecient meaning it should not be in fraction or decimal form.
example. ( ½ , ¾ )
sum = ½ + ¾
= ⅝
product = ½ x ¾
= ⅜
x² - sumx + product = 0 → x² - ⅝x + ⅜ = 0
because there is a fraction and i just mentioned a while ago that we cant have fraction we'll have to do this:
8 (x² - ⅝x + ⅜ = 0)
multpily everthing by 8 (the denominator), and the answer should be:
8x² -5x + 3 = 0
Finally, I'm finish. I think I covered everything. Wow it took me forever to finish it sigh* im finally done!! yeeheyy!! lol.. and yeah for the next scribe or iunno what they call it.. It will be the pretty girl behind me.. sophia.. i mean Ms. Paulette ------- ...... lol.. yeah I know you already knew that your next but goodluck friendship... love you!!
Ok.. now i need to finish doing some stuff and man doing this blog is kind of hard and I probably made some mistakes (Im kinda not in me today..lol) .. so uhmm if i had some mistakes, anyone can tell me and i'll try to correct it.. thank you very much pipol!! =P
posted by Remyshire @ 8:42 PM
0 Comments:
Post a Comment
<< Home