8.
If a and b are the roots of x2 – 3x + p = 0 and c, d are roots of x² - 12x + q = 0,
where a, b, c, d form a GP. Prove that (q + p): (q- p) = 17:15.
Answers
Answered by
0
Step-by-step explanation:
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
Similar questions