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How did you determine the coefficients so arbitrarily? The answer is correct though but I think that's cheating.
Using factor theorem is a very bad way to solve this kind of equation.
Anyways 200 sats for the good effort and somehow getting the correct answer :)
I followed
from the link I posted.
that's okay, but the rational root test link shows you solved the equation using a solver which is not okay, had you not posted the link and only written "rational root test", I might not have figured it out, but since you did, it puts a wrong impression
it's okay to use a solver once you understand the method, but citing is not always necessary! (another lesson I learnt the hard way)
but another 200 sats for being honest and using formulas the correct way!
Since squaring both sides introduced false solutions, we have to check the four solutions above by inserting them into the original equation, which shows only two of them a true solutions:
and
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Oh, this is a better strategy: https://www.mathportal.org/formulas/algebra/solalgebric.php
With a1=0,a2=−10,a3=−1,a4=20 the cubic equation becomes
and with y1=−9 (rational root test) the quadratic equations become
The solutions are
and