Answer variants:
real and equal
no real root
real and unequal roots
Show that the equation \(x^2(a^2 + b^2) + 2x(ac + bd) + c^2 + d^2 = 0\) has no real roots. If \(ad = bc\), then verify that the roots are real and equal.
Answer:
Here, \(a =\) , \(b =\) , \(c =\)
\(\Delta = b^2 - 4ac =\)
Since \(\Delta =\) , the given equation has .
If \(ad = bc\), then \(\Delta =\) .
Therefore, if \(ad = bc\) and so the roots will be .
Hence, we proved.