Polynomials Q: help needed pls! (1 Viewer)

[jjnfg]

I have a problem with these questions; if anyone knows how to do it I would be very grateful!!

1) If the sum of two roots of x (to the power 4) + 2x (to the power 3) - 8x (squared) - 18x - 9=0 is 0, find the roots of the equation.

2) Solve 2cos (cubed)x + cos (squared) x - cosx =0 for x is more than or equal to o degrees and less or equal to 360 degrees.

Thanks heaps.

 

[Harimau]

1) Can't be bothered to such long things. Just let the roots be A, -A, B and C. From then on use the sum of roots, the product of roots, the sum of roots three at a time, the sum of roots two at a time, and use simultaneous equations.

2) Factorise the Cosx:

cosx (2cos^2x + cosx - 1) =0
cosx (2cosx -1)(cosx+1)=0

Solve normally from there for cosx= 0, cosx=1/2, cosx= -1 with attention to the domain. Make sure your end result is between 0 and 360 degrees, and they will all be exact value as well.

 

[Toodulu]

for the first one, i tested the divisors of the constant term, -1 and -3 were roots
i did P(x) = (x+3) (x+1) (x -A) (x-B) where A and B are the 2 other roots
so P(x) = (x^2+4x+3) (x^2-2x-3) by inspection
and then i factorised it
ie. P(x) = (x+3)(x+1)(x-3)(x+1)
roots are 3, -3, -1, -1

 

[jjnfg]

thankx so much for ure help...

 

[timeisonmyside]

how poor at maths are u

 

[abdooooo!!!]

not everyone is as smart as you are... if you're not helping at least don't be so judgmental