Posted by preet0099 help me ! on Wednesday, December 5, 2012 at 7:49am.
proof that the equation
x^2(a^2+b^2)+2x(ac+bd)+(C^2+d^2)=0 has no real roots.

maths  Steve, Wednesday, December 5, 2012 at 11:24am
the discriminant is
4(ac+bd)^2  4(a^2+b^2)(c^2+d^2)
junk the 4, as it does not change things, and you have
a^2c^2 + 2abcd + b^2d^2  a^2c^2  a^2d^2  b^2c^2  b^2d^2
= 2abcd  a^2d^2  b^2c^2
= (adbc)^2
since that is always negative, there are no real roots.
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