Question

If alpha beta are the zeros of the polynomial x2 -x+6 then find the value of i) 1/alpha+1/beta

Answer 1

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❚ QuEstiOn ❚

# If $\alpha$ and $\beta$ are the zeros of the polynomial f(x)=X² -X+6

Then find the value of $(\dfrac{1}{\alpha}+\dfrac{1}{\beta})$ = ?

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❚ ANsWeR ❚

✺ Given :

• zeroes are $\alpha$ and $\beta$

✺ To FinD:

• $(\dfrac{1}{\alpha}+\dfrac{1}{\beta})$ = ?

✺ Explanation :

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If $\alpha$ and $\beta$ are the Zeroes of the Polynomial P(X) then it can be written as ,

✏ X²- $(\alpha+\beta)$X + $(\alpha\beta)$

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Now comparing the polynomial f(X)=X² -X+6 with X²- $(\alpha+\beta)$X + $(\alpha\beta)$ we get ,

:$\longrightarrow (\alpha+\beta)$ = 1

:$\longrightarrow \alpha\beta$ = 6

$\therefore \:\:\:\ \ {\dfrac{1}{\alpha}+\dfrac{1}{\beta}}$

$\implies \ \ {\dfrac{1}{\alpha}+\dfrac{1}{\beta}}$

$\implies \ \ {\dfrac{\beta+\alpha}{\alpha\beta}}$

$\implies \ \ {\dfrac{\alpha+\beta}{\alpha\beta}}$

( putting the values of $(\alpha+\beta)=1$ and $\alpha\beta$=6)

$\implies \ \ {\dfrac{1}{6}}$

✺ Therefore :

✏ $\ \ {\boxed{\red{\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{1}{6}}}}$

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Answer 2

If , α and β are the Zeroes of the Polynomial P(X) then it can be written as ,

=> X²- (α+β) X + (αβ)

Now comparing the polynomial f(X)=X² -X+6 with X²- (α+β) X + (αβ) we get ,

⟶(α+β) = 1

⟶αβ = 6

$</p><p>\tt{\red{\therefore{\dfrac{1}{\alpha}+\dfrac{1}{\beta}}}}}$

$</p><p>\tt{\blue{\implies \ \ {\dfrac{\alpha+\beta}{\alpha\beta}} = \dfrac{1}{6}}}$

$</p><p> {\boxed{\orange{\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{1}{6}}}}$