Find ax^p + bx^q+ c to be polynomial p & q are ??????
Answers
Answered by
0
Answer:
Explanation:
We have x
2
+px+q=0....(i)
x
2
+rx+s=0....(ii)
Let D
1
and D
2
be the discriminants of equations (i) and (ii). Then
D
1
=b
2
−4ac=p
2
−4q
similarly,
D
2
=r
2
−4s
⇒D
1
+D
2
=p
2
−4q+r
2
−4s=(p
2
+r
2
)−4(q+s)
⇒D
1
+D
2
=p
2
+r
2
−4(
2
pr
)[∵pr=2(q+s)∴q+s=
2
pr
]
⇒D
1
+D
2
=p
2
+r
2
−2pr=(p−r)
2
≥0
At least one of D
1
and D
2
is greater than or equal to zero
At least one of the two equations has real roots.
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2
Answer:
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