If a and b are the roots of the equation 2x square
− 7x + p= 0 and c and d are the roots of the
equation 2xsquare
− 8x+ q= 0 , where a,b,c,d form a G.P then find the value of q-p/q+p
Answers
Solution
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Correct option is
D
−2
Given quadratic equation are 2x
2
+x+k=0 and x
2
+
2
x
−1=0
Since the given equation has two roots in common, so from the condition
a
2
a
1
=
b
2
b
1
=
c
2
c
1
⇒
1
2
=
2
1
1
=
−1
k
⇒k=−2
Hence, option D is correct.
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Answer:
Given Quadratic equations are x
2
−3x+p=0 x
2
−12x+q=0 whose roots are a,b and c,d respectively.
Let a=A, b=Ar, c=Ar
2
, d= Ar
3
Then a,b,c,d form aGP with a common ratio r
Now,a+b=3
ab=p
c+d=12
cd=q
a+b=A(1+r)=3
A=
1+r
3
c+d = Ar
2
(1+r)
From these two equations
3r
2
=12
r=±2
Let r=2
A=
1+r
3
=1
a=A=1
b=Ar=2
c= Ar
2
=4
d = Ar
3
=8
p−q
p+q
=
32−2
32+2
=
15
17
Let r=−2
A=
1−r
3
=−3
a=−3
b=Ar=6
c=Ar
2
=−12
d=Ar
3
=24
q−p
q+p
=
−288+18
−288−18
=
−270
−306
=
15
17
Hence, Proved