SOLUTION: tell the nature of the solution by using the discriminant and then solve to find the exact root Factor when Possible 2x^2+7x+3=0

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Question 1068617: tell the nature of the solution by using the discriminant and then solve to find the exact root
Factor when Possible
2x^2+7x+3=0
Found 4 solutions by josgarithmetic, josmiceli, ikleyn, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Look at previous example.

Here, discriminant is 49-4%2A2%2A3=49-24=25=5%5E2.

You do the rest.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E2+%2B+7x+%2B+3+=+0+
The quadratic formula is
x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
The discriminant is
+b%5E2+-+4%2Aa%2Ac+
and
+a+=+2+
+b+=+7+
+c+=+3+
+b%5E2+-++4%2Aa%2Ac+=+7%5E2+-+4%2A2%2A3+
+b%5E2+-+4%2Aa%2Ac+=++49+-+24+
+b%5E2+-+4%2Aa%2Ac+=+25+
-----------------------
If the discriminant is positive, there are 2 real roots
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+x+=+%28+-7+%2B-+sqrt%28+25+%29%29%2F%282%2A2%29+
+x+=+%28+-7+%2B+5+%29%2F4+
+x+=+-1%2F2+
and, taking the negative square root of +25+,
+x+=+%28+-7+-+sqrt%28+25+%29%29%2F%282%2A2%29+
+x+=+%28+-7+-+5+%29%2F4+
+x+=+-12%2F4+
+x+=+-3+
---------------------------
From these results, I can write the factors
+%28+x+%2B+1%2F2+%29%2A%28+x+%2B3+%29+=+0+
+x%5E2+%2B+%281%2F2%29%2Ax+%2B+3x+%2B+3%2F2+=+0+
+x%5E2+%2B+%287%2F2%29%2Ax+%2B+3%2F2+=+0+
Multiply both sides by +2+
+2x%5E2+%2B+7x+%2B+3+=+0+
OK

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
See the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".



Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
tell the nature of the solution by using the discriminant and then solve to find the exact root
Factor when Possible
2x^2+7x+3=0
Discriminant: matrix%281%2C5%2C+b%5E2+-+4ac%2C+%22=%22%2C+7%5E2+-+4%282%29%283%29%2C+%22=%22%2C+25%29

With the discriminant being a PERFECT SQUARE, then 



Now that you have the discriminant, you can continue to solve using the quadratic equation formula, but since the TRINOMIAL can be factored,

it's easier to do so to get the exact roots.

, and we then get: