71http://en.wikipedia.org/wiki/Complex_conjugate_root_theorem
Q) prove that the img. roots of a quadratic eqn. 'ax2 + bx + c = 0' always occur in conjugate pairs. where a,b,c E R
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71
36the link dosen't take us to the proof......... !!
well the second thread is quite interesting...!!
262let one root be imaginary and the other be real .
thus sum of roots will be imaginary = -b/a
but b and a are real numbers.
contradiction.
3yup aditya is correct.
since the sum is real, and one root is complex, this implies that the other root is complex too.
z + z' = real iff they are a conjugate pair.
36Look at my question first
the term 'conjugate pairs' has been used
u 2 proved that the other root will be imaginary...
as if a root is (2 + 3i) and the other is (-3i + 8). They too satisfy that Z1 + Z2 = real but r not in conjugate pairs
Here z1 + z2 = Real and at the same time z1.z2 = Real which is possible only when they occur in conjugate pairs...!!
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well one other simple way could hv been
x = -b ± √b2 - 4ac2a
now, if D < 0 or that b2 - 4ac < 0 where a,b,c E R
or, x = -b2a ± √b2 - 4ac2a
which shows if they are imaginary then will occur in conjugate paris...