SOLUTION: {{{3y^2+7y+1=0}}}

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Question 215248: 3y%5E2%2B7y%2B1=0
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
3y%5E2%2B7y%2B1=0

The following will solve the quadratic equation with the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=3, b=7 and c=1.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 3y%5E2%2B7y%2B1+=+0) has the following solutons:

y%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=%287%29%5E2-4%2A3%2A1=37.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+37+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%287%29%2Bsqrt%28+37+%29%29%2F2%5C3+=+-0.152872911616963
y%5B2%5D+=+%28-%287%29-sqrt%28+37+%29%29%2F2%5C3+=+-2.18046042171637

Quadratic expression 3y%5E2%2B7y%2B1 can be factored:
3y%5E2%2B7y%2B1+=+3%28y--0.152872911616963%29%2A%28y--2.18046042171637%29
Again, the answer is: -0.152872911616963, -2.18046042171637. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B7%2Ax%2B1+%29



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J