.Prove that the equation x2(p2+q2) + 2x(pr+qs) + r2+ s2=0 has no real roots. If ps=qr,then
show that the roots are real and equal.
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Answered by
2
Answer:
Equation px
2
+2qx+r=0 and qx
2
−2
pr
x+q=0 have real roots, then
b
2
−4ac≥0 for both equations
From first
4q
2
−4pr≥0⇒q
2
≥pr ...............(1)
and from second
4(pr)−4q
2
≥0 (for real root)
⇒pr≥q
2
...............(2)
From (1) and (2), we get result q
2
=pr
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Answer:
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