SOLUTION: Please help me use the quadratic formula to solve the following. Leave irrational roots in the simplest radical form. {{{3m^2 + m - 2 = 0}}} {{{5p^2 + 3p - 2 = 0}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please help me use the quadratic formula to solve the following. Leave irrational roots in the simplest radical form. {{{3m^2 + m - 2 = 0}}} {{{5p^2 + 3p - 2 = 0}}}       Log On


   

Question 695875: Please help me use the quadratic formula to solve the following. Leave irrational roots in the simplest radical form.
3m%5E2+%2B+m+-+2+=+0
5p%5E2+%2B+3p+-+2+=+0

Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic formula is x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
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Using 3m%5E2%2Bm-2=0, a is 3, b is 1 and c is -2
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m=%28-1%2B-sqrt%281%5E2-4%283%29%28-2%29%29%29%2F%282%2A3%29
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m+=+%28-1%2B-sqrt%281%2B24%29%29%2F%286%29
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m+=+%28-1%2B-5%29%2F6
Two solutions
m = %28-1%2B5%29%2F6, so highlight_green%28m+=+4%2F6+=+2%2F3%29
m = %28-1-5%29%2F6, so highlight_green%28m+=+-6%2F6+=+-1%29
The solutions make sense because it factors as (3m-2)(m+1)=0
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Using 5p^2 + 3p - 2 = 0
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p+=%28-3%2B-sqrt%283%5E2-4%285%29%28-2%29%29%29%2F%282%2A5%29
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p+=+%28-3%2B-sqrt%289%2B40%29%29%2F10
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p+=+%28-3%2B-7%29%2F10
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Two solutions
p = %28-3%2B7%29%2F10, so highlight_green%28p+=+4%2F10+=+2%2F5%29
p = %28-3-7%29%2F10, so highlight_green%28p+=+-10%2F10+=+-1%29
The solutions make sense because it factors as (5p-2)(p+1)=0
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