if alpha and beta are the roots of x^2-2x+3=0 then the quadratic equation whose roots are apha^2 and beta ^2
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0
Answer:
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Step-by-step explanation:
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Answered by
2
Solution
The correct option is C
x
2
−
3
x
+
2
=
0
Given
α
,
β
are roots of the equation
x
2
−
2
x
+
3
=
0
⇒
α
2
−
2
α
+
3
=
0
⋯
(
1
)
and
β
2
−
2
β
+
3
=
0
⋯
(
2
)
⇒
α
2
=
2
α
−
3
⇒
α
3
=
2
α
2
−
3
α
⇒
P
=
(
2
α
2
−
3
α
)
−
3
α
2
+
5
α
−
2
⇒
P
=
−
α
2
+
2
α
−
2
⇒
P
=
3
−
2
=
1
[Using (1)]
Similarly, we have
Q
=
2
.
P
+
Q
=
3
and
P
Q
=
2
Hence, the required equation is
x
2
−
3
x
+
2
=
0
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