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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:

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\frac{7}{3}

- \frac{7}{3}

\frac{3}{7}

- \frac{3}{7}

answer is D.

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Detailed Solution

Given that

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 if a polynomial is of the form

a x^{2} + bx + c,

then the sum of roots

= \frac{- b}{a}

and the product of roots

= \frac{c}{a} .

From the given polynomial,

α + β = - \frac{3}{4}

and

αβ = \frac{7}{4}

Therefore,

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

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

Hence,

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

.
Hence, option 4 is correct.

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