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WBJEE 2016 Math Solved Paper
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© examsnet.com
Question : 61
Total: 75
If α and β are roots of a
x
2
+ bx + c = 0 then the equation whose roots are
α
2
and
β
2
is
a
2
x
2
−
(
b
2
−
2
a
c
)
x
+
c
2
= 0
a
2
x
2
+
(
b
2
−
a
c
)
x
+
c
2
= 0
a
2
x
2
+
(
b
2
+
a
c
)
x
+
c
2
= 0
a
2
x
2
+
(
b
2
+
2
a
c
)
x
+
c
2
= 0
Validate
Solution:
Let y = x^2 ⇒ x =
√
y
putting
√
y
in the given equation
ay + b
√
y
+ c = 0 ⇒ b
√
y
= -ay - c ⇒
b
2
y =
a
2
y
2
+
c
2
+ 2acy
⇒
a
2
y
2
- (
b
2
- 2ac) y +
c
2
= 0
So the required quadratic equation is
a
2
x
2
- (
b
2
- 2ac) x +
c
2
= 0
© examsnet.com
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