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Answer variants:
real and unequal roots
real and equal
no real root
Prove that the equation \(x^2(p^2 + q^2) + 2x(pr + qs) + r^2 + s^2 = 0\) has no real roots. If \(ps = qr\), then show that the roots are real and equal.
Answer:
Here, \(a =\) , \(b =\) , \(c =\)
\(\Delta = b^2 - 4ac =\)
Since \(\Delta =\) , the given equation has .
If \(ps = qr\), then \(\Delta =\) .
Therefore, if \(ps = qr\) and so the roots will be .
Hence, we proved.