A lvl complex numbers Qns

Miguelogy SG

Hi guys,i've had problem with this tys qns:

The equation az^4+bz^3+cz^2+dz+e=0 has a root z=ki, where k is real and non-zero. Given that the coefficients of the eqn are real, show that ad^2+b^2e=bcd.

I noe that z=-ki is another root, correct me if im wrong, but how to go on ?

jayh272416 SG

sub ki into the equation

you get ak^4-bk^3i-ck^2+dki+e=0

comparing real and imaginary parts, you have dk=bk^3

thus k^2=d/b

also, ak^4-ck^2+e=0

thus a(d/b)^2-c(d/b)+e=0

multiplying b^2 to everything you have

ad^2-bcd+b^2e=0 and rearranging gets

ad^2+b^2e=bcd

wee_ws SG

Hi Miguelogy,

As you prepare for your H2 Maths exam come early Nov, be sure to read practical tips at:

http://sgforums.com/forums/2297/topics/356377?page=4#post_10370939

Jiayou!

Cheers,
Wen Shih