If α and β are the zeroes of the polynomial 4x2+3x+7, then α1+β1 is equal to:

Given: α,β are zeroes of the polynomial 4x2+3x+7To find the value of α1+β1We know that equation ax2+bx+c=0Then sum of roots =a−b and product of roots=acFrom the given quadratic equation,α+β=−43 and αβ=47Therefore, α1+β1=αβα+β=47−43=−73⇒α1+β1=−73

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If and are the zeroes of the polynomial 4x^{2} + 3x + 7, the

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If $α$ and $β$ are the zeroes of the polynomial $4 x^{2} + 3 x + 7$ , then $\frac{1}{α} + \frac{1}{β}$ is equal to:

\frac{7}{3}

- \frac{7}{3}

\frac{3}{7}

- \frac{3}{7}

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Sebastian Discussed

α

and

β

are the zeroes of the polynomial

4 x^{2} + 3 x + 7

, then

\frac{1}{α} + \frac{1}{β}

is equal to:

13 mins ago

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13 mins ago

Text solutionVerified

Given:

α, β

are zeroes of the polynomial

4 x^{2} + 3 x + 7

To find the value of

\frac{1}{α} + \frac{1}{β}

We know that equation $a x^{2} + b x + c = 0$

Then sum of roots $= \frac{- b}{a}$ and product of roots $= \frac{c}{a}$

From the given quadratic equation,

α + β = - \frac{3}{4}

and

α β = \frac{7}{4}

Therefore,

\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β}

= \frac{- \frac{3}{4}}{\frac{7}{4}} = - \frac{3}{7}

\Rightarrow \frac{1}{α} + \frac{1}{β} = - \frac{3}{7}

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Question Text	If $α$ and $β$ are the zeroes of the polynomial $4 x^{2} + 3 x + 7$ , then $\frac{1}{α} + \frac{1}{β}$ is equal to:
Answer Type	Text solution:1
Upvotes	150

If α and β are the zeroes of the polynomial 4x2+3x+7, then α1​+β1​ is equal to:

Text solutionVerified

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If $α$ and $β$ are the zeroes of the polynomial $4 x^{2} + 3 x + 7$ , then $\frac{1}{α} + \frac{1}{β}$ is equal to: