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Assertion :If , , are the zeroes of x^3-2x^2+qx-r and +=0, th

Question

Assertion :If $α, β, γ$ are the zeroes of $x^{3} - 2 x^{2} + q x - r$ and $α + β = 0$ , then $2 q = r$
Reason :If $α, β, γ$ are the zeroes of $a x^{3} + b x^{2} + c x + d$ , then $α + β + γ = - \frac{b}{a}, α β + β γ + γ α = \frac{c}{a}, α β, γ = - \frac{d}{a}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion is correct but Reason is incorrect

Assertion is incorrect but Reason is correct

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Benjamin Discussed

Assertion :If

α, β, γ

are the zeroes of

x^{3} - 2 x^{2} + q x - r

and

α + β = 0

, then

2 q = r

Reason :If

α, β, γ

are the zeroes of

a x^{3} + b x^{2} + c x + d

, then

α + β + γ = - \frac{b}{a}, α β + β γ + γ α = \frac{c}{a}, α β, γ = - \frac{d}{a}

7 mins ago

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Text solutionVerified

Clearly, Reason is true. [Standard Result]

α + β + γ = - (- 2) = 2 \Rightarrow 0 + γ = 2 ∴ γ = 2

α β γ = - (- r) = r ∴ α β (2) = r \Rightarrow α β = \frac{r}{2}

α β + β γ + γ α = q \Rightarrow \frac{r}{2} + γ (α + β) = q \Rightarrow \frac{g}{2} + γ (0) = q

\Rightarrow γ = 2 q ∴

Assertion is true
Since, Reason gives Assertion

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Question Text	Assertion :If $α, β, γ$ are the zeroes of $x^{3} - 2 x^{2} + q x - r$ and $α + β = 0$ , then $2 q = r$ Reason :If $α, β, γ$ are the zeroes of $a x^{3} + b x^{2} + c x + d$ , then $α + β + γ = - \frac{b}{a}, α β + β γ + γ α = \frac{c}{a}, α β, γ = - \frac{d}{a}$
Answer Type	Text solution:1
Upvotes	151