SOLUTION: i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true? a=3x^2+ b=8x+ c=2

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Question 47789: i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true?
a=3x^2+
b=8x+
c=2
Found 2 solutions by stanbon, venugopalramana:
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
a=3x^2+
b=8x+
c=2
----------------------
The a,b,and c are the coefficients of the terms,
not the terms themselves.
a=3
b=8
c=2
----------
Then the determinant is b^2-4ac = 64-4*3*2=40
Since this is greater than zero the quadratic has
two real zeroes. The zeroes may be irrational and
still be real.
Consider the following:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B8x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A3%2A2=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+40+%29%29%2F2%5C3+=+-0.279240779943873
x%5B2%5D+=+%28-%288%29-sqrt%28+40+%29%29%2F2%5C3+=+-2.38742588672279

Quadratic expression 3x%5E2%2B8x%2B2 can be factored:
3x%5E2%2B8x%2B2+=+3%28x--0.279240779943873%29%2A%28x--2.38742588672279%29
Again, the answer is: -0.279240779943873, -2.38742588672279. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B8%2Ax%2B2+%29

Hope this helps.
Cheers,
Stan H.


























Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true?
a=3x^2+
b=8x+
c=2
3x^2+8x+2=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+
x+=+%28-8+%2B-+sqrt%28+64-24+%29%29%2F%286%29+
x+=+%28-8+%2B-+2%2Asqrt%2810%29%29%2F%286%29+
x+=+%28-4+%2B-+sqrt%2810%29%29%2F%283%29+
yes you are correct.the roots are irrational