Find all the roots of 2y^4 - 9y^3 + 14y^2 + 6y - 63

Question

brinazarski · Answer

My answer was -1.5 and 3. Is that correct?

perl · Answer

checked wolfram?

brinazarski · Answer

No... don't know what that is...

hartnn · Answer

u are correct about real roots, but don't u need to find imaginary roots also ? http://www.wolframalpha.com/input/?i=roots+of+2y%5E4+-+9y%5E3+%2B+14y%5E2+%2B+6y+-+63 wolfram agrees with your real roots.

brinazarski · Answer

How would you find the imaginary roots without wolfram?

hartnn · Answer

how did u get real roots ?

brinazarski · Answer

Calculator lol. Graphed 2x^4 - 9x^3 + 14y^2 +6y and 63, then found the intersections

hartnn · Answer

if u can use calculator, u can certainly use wolfram.....

brinazarski · Answer

but not in school on a test...

hartnn · Answer

can u divide polynomials ?

brinazarski · Answer

Eh... I don't know... haven't done it in awhile...

brinazarski · Answer

Would that get me the imaginary roots?

hartnn · Answer

yup, u divide your polynomial with (x+1.5)(x-3)
u get a quadratic equation.,
solve that using quadratic formula.
u get 2 imaginary roots also

brinazarski · Answer

So in all cases, when you find the roots, you divide the polynomial by (x-root)(x-otherroot) and then do the rest of the steps to double check that there are no imaginaries?

hartnn · Answer

not all....
here u got some roots(2), to find other roots, divide by all (x-root)'s to get an equation with lesser degree, so that it can be solved easily.

brinazarski · Answer

Okay, I think I understand :) Thank you!

hartnn · Answer

welcome :)