If the roots of the equation x 2- bx - ac -0 are - - and roots of the equation x 2- ax - bc -0 are - y then the value of - - Y respectively Previous year JEE questionA- C - a - bB- None of theseC- a- b- cD- b - c - a

The correct option is A c, a, b α + β = b ...(1) αβ = ac ...(2) α + γ = a ...(3) αγ = bc ...(4) (1) (3) ⇒β γ = a ...

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Standard XI

Mathematics

Inequalities Involving Modulus Function

If the roots ...

Question

If the roots of the equation $x^{2} + b x + a c = 0 a r e α, β$ and roots of the equation $x^{2} + a x + b c = 0$ are $α, γ$ then the value of $α, β, γ$ respectively (Previous year JEE question)

a, b, c

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b, c, a

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c, a, b

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None of these

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Solution

The correct option is C c, a, b
$α + β = - b . . . (1)$
$α β = a c . . . (2)$
$α + γ = - a . . . (3)$
$α γ = b c . . . (4)$
$(1) - (3) \Rightarrow β - γ = a - b . . . (5)$
$\frac{(2)}{(4)} \Rightarrow \frac{β}{γ} = \frac{a}{b}$
$β = \frac{a γ}{b} . . . (6)$
putting the value of $β$ in (5)
$\frac{a γ}{b} - γ = a - b \Rightarrow γ \frac{(a - b)}{b} = (a - b) ∴ γ = b ∴ β = a a n d α = c$

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Similar questions

Q. If the roots of the equation

x^{2} + b x + a c = 0 a r e α, β

and roots of the equation

x^{2} + a x + b c = 0

are

α, γ

then the value of

α, β, γ

respectively (Previous year JEE question)

Q. lf the roots of equation

x^{2} + b x + a c = 0

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and

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, the roots of the equation

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are

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Q. If

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x^{2} + b x + c = 0

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Q. Statement I: lf

α, β

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x^{2} - a x + b = 0

, then the equation whose roots are

\frac{α + β}{α}, \frac{α + β}{β}

b x^{2} - a^{2} x + a^{2} = 0

Statement II: lf

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x^{2} - b x + c = 0

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If the roots of the equation x2+bx+ac=0 are α,β and roots of the equation x2+ax+bc=0 are α,γ then the value of α,β,γ respectively (Previous year JEE question)

The correct option is C c, a, b α+β=−b ...(1) αβ=ac ...(2) α+γ=−a ...(3) αγ=bc ...(4) (1)−(3)⇒β−γ=a−b ...(5) (2)(4)⇒βγ=ab β=aγb ...(6) putting the value of β in (5) aγb−γ=a−b⇒γ(a−b)b=(a−b) ∴γ=b ∴β=a and α=c

If the roots of the equation $x^{2} + b x + a c = 0 a r e α, β$ and roots of the equation $x^{2} + a x + b c = 0$ are $α, γ$ then the value of $α, β, γ$ respectively (Previous year JEE question)