4) If the equation x² -px + q = 0 and x- ax + b = 0 have a common root and thesecond equation has equal roots then
1) aq = 2(b + p)
2) aq = b + a 3) ap = 2(b + 9)
4) ap = b + a
Answers
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Step-by-step explanation:
(i).
a,b,c in G.P. ⇒b
2
−ac=0
Δ
1
=4(b
2
−ac)=0 ∴ It has equal roots
∴ α+α=−
a
2b
or α=−
a
b
Since the two equations have common roots therefore
α=−b/a must also be a root of 2nd equation.
∴ d(−
a
b
)
2
+2e(−
a
b
)+f=0
or
a
d
.
a
b
2
+
b
2e
(
a
−b
2
)+
c
f
c=0 (Note)
or
a
d
.
a
b
2
−
b
2e
(
a
b
2
)+
c
f
(
a
b
2
)=0
∵ b
2
=ac
or
a
d
−
b
2e
+
c
f
=0 or
a
d
,
b
e
,
c
f
are in A.P.
Another form : Assume that p,q,r are in G.P., so that q
2
=pr which implies that roots of 2nd equation are equal and rest as above.
How satisfied are you with the answer?
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