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CMAT 2016 Solved Question Paper
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© examsnet.com
Question : 6
Total: 100
One of the roots of the equation
x
2
+
k
x
−
4
=
0
is equal to 1 and other equation
x
2
+
k
x
+
k
2
= 0 has equal roots.
Find the equation whose roots are k and
k
2
.
4
x
2
−
x
+
27
=
0
4
x
2
−
21
x
+
27
=
0
x
2
−
21
x
+
7
=
0
4
x
2
−
21
x
+
7
=
0
Validate
Solution:
(b) Since, x = 1 is a root of equation.
x
2
+ kx - 4 = 0
⇒
1
2
+ k × 1 - 4 = 0 ⇒ k = 3
Equation
x
2
+ kx +
k
2
= 0 has equal roots.
By Sridharacharya method,
For equal roots,
b
2
- 4ac = 0
⇒
k
2
- 4 × 1 +
k
2
= 0
⇒
3
2
-4
k
2
= 0
[∵ k = 3]
⇒ 9 - 4
k
2
=0 ⇒
k
2
=
9
4
∴ Required equation,
x
2
−
(
k
+
k
2
)
x
+
k
k
2
= 0
⇒
x
2
−
(
9
4
+
3
)
x
+
9
4
×
3
= 0
⇒ 4
x
2
- 21x + 27 = 0
© examsnet.com
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