SOLUTION: Find all solutions of the equation. (Enter all answers including repetitions. Enter your answers as a comma-separated list.) 6x^5 + 43x^4 + 37x^3 − 30x^2 = 0

Algebra ->  Rational-functions -> SOLUTION: Find all solutions of the equation. (Enter all answers including repetitions. Enter your answers as a comma-separated list.) 6x^5 + 43x^4 + 37x^3 − 30x^2 = 0      Log On


   

Question 1113493: Find all solutions of the equation. (Enter all answers including repetitions. Enter your answers as a comma-separated list.)
6x^5 + 43x^4 + 37x^3 − 30x^2 = 0
Found 3 solutions by josgarithmetic, Alan3354, MathLover1:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
Factorize the x%5E2;
x%5E2%286x%5E3%2B43x%5E2%2B37x-30%29=0
and you see a root of 0, with multiplicity 2.
You then will have several possible roots to test using synthetic division (Rational Roots Theorem). You should find ONE rational root of -6, and the next two you can find using formula for solution of quadratic equation. (Or try factorizing the quadratic if possible).

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If I find all the solutions, can you make the "comma separated list?"
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Why include that? Do you need the typing practice?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E5+%2B+43x%5E4+%2B+37x%5E3+-30x%5E2+=+0+....factor
x%5E2+%286x%5E3+%2B+43x%5E2+%2B+37x-+30%29=+0+
x%5E2++%286+x%5E3%2B36x%5E2%2B+7x%5E2%2B42x+-5x-30%29+=+0
x%5E2++%28%286+x%5E3%2B36x%5E2%29%2B%28+7x%5E2%2B42x%29+-+%285x%2B30%29%29+=+0
x%5E2+%28x+%2B+6%29+%286+x%5E2+%2B+7+x+-+5%29+=+0
x%5E2+%28x+%2B+6%29+%286+x%5E2+-3x%2B+10x+-+5%29+=+0
x%5E2+%28x+%2B+6%29+%28%286+x%5E2+-3x%29%2B+%2810x+-+5%29%29+=+0
x%5E2+%28x+%2B+6%29+%283x%282x+-1%29%2B+5%282x+-+1%29%29+=+0
x%5E2+%28x+%2B+6%29+%282x+-+1%29+%283x+%2B+5%29+=+0


if x%5E2++=+0=>x=0
if +%28x+%2B+6%29++=+0 => x=-6
if +%282x+-+1%29++=+0=> x=1%2F2
if +%283x+%2B+5%29+=+0=> x=-5%2F3
so, solutions are:x=-6,x=-5%2F3,x=0,x=1%2F2