If the ratio of the roots of the equation x² - px +q = 0 be
a:b, prove that, p²ab=q(a + b)2. Hence find the
condition of equal roots of the given equation.
Answers
Answered by
0
Step-by-step explanation:
If x
2
−2px+8p−15=0 has equal roots, then p equals
EASY
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ANSWER
let the root be α then
2α=2P⇒α=P.....(1)
and
α
2
=8P−15=8α−15
α
2
=3α−5α+15=0
⇒(α−3)(α−5)=0
α=3 or 5⇒P=3 or 5
Answer By
Answered by
0
Step-by-step explanation:
Let α,β be the roots of equation x
2
+px+q=0 and let γ,δ be the roots of equation x
2
+bx+c=0
Then, α+β=−p,αβ=q
and γ+δ=−b,γδ=c
Given,
β
α
=
δ
γ
Applying componendo-dividendo
α−β
α+β
=
γ−δ
γ+δ
⇒
(α−β)
2
(α+β)
2
=
(γ−δ)
2
(γ+δ)
2
⇒
α
2
+β
2
−2αβ
p
2
=
γ
2
+δ
2
−2γδ
b
2
⇒
(α+β)
2
−4αβ
p
2
=
(γ+δ)
2
−4γδ
b
2
⇒
p
2
−4q
p
2
=
b
2
−4c
b
2
⇒p
2
c−b
2
q=0`
Hence, option 'A' is correct.
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