SOLUTION: Hello, I need help solving this equation please. It is supposed to be written in quadratic form, but I do not know how to write it out either. {{{ a^5+6a^4+5a^3=0 }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello, I need help solving this equation please. It is supposed to be written in quadratic form, but I do not know how to write it out either. {{{ a^5+6a^4+5a^3=0 }}}      Log On


   

Question 729978: Hello, I need help solving this equation please. It is supposed to be written in quadratic form, but I do not know how to write it out either.
+a%5E5%2B6a%5E4%2B5a%5E3=0+
Found 4 solutions by Alan3354, hoomanc, ankor@dixie-net.com, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5E5%2B6a%5E4%2B5a%5E3=0+
a%5E3%2A%28a%5E2%2B6a%2B5%29+=+0+
a = 0, 0, 0
---------------
a%5E2%2B6a%2B5=0+
Solve by factoring
a = -5, -1

Answer by hoomanc(14) About Me  (Show Source):
You can put this solution on YOUR website!
factor +a%5E3+ from the eq. like +a%5E3%28a%5E2%2B6a%2B5%29=0+ so either
+a%5E3=0+ or +a%5E2%2B6a%2B5=0+ should be check.
for first one +a=0+ and for the second part refer to the answer for question number
( www.algebra.com/cgi-bin/jump-to-question.mpl?question=729964 ).

for final check, your answers should be:
0
-5
-1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5E5%2B6a%5E4%2B5a%5E3=0+
Factor out a^3
+a%5E3%28a%5E2%2B6a%2B5%29=0+
Factor again
a^3(a+5)(a+1) = 0
three solutions
a = 0
a = -5
a = -1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Factor out



Then factor the quadratic. You will then have 5 zeros, as you would expect for a fifth degree polynomial equation. 3 of them will be zero and the other two will be the zeros of the quadratic factor. Hint: 5 + 1 = 6 and 5 times 1 = 5.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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