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If $α$ and $β$ are the zeroes of the polynomial $f (x) = 6 x^{2} - 3 - 7 x$ , then $(α + 1) (β + 1)$ is equal to

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\frac{2}{5}

\frac{5}{3}

\frac{3}{5}

\frac{5}{2}

answer is B.

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Detailed Solution

Given,

α

and

β

are the zeroes of the polynomial

f (x) = 6 x^{2} - 3 - 7 x

.
We need to find the value of

(α + 1) (β + 1) .

We know that,
Sum of roots

= \frac{- b}{a}

Product of roots

= \frac{c}{a}

α

β

are the zeroes of the quadratic polynomial

f (x) = 6 x^{2} - 3 - 7 x

, then,

(α + β) = \frac{- b}{a} = - \frac{- 7}{6} = \frac{7}{6},

αβ = \frac{c}{a} = \frac{- 3}{6} = - \frac{1}{2}

Now,

(α + 1) (β + 1) = αβ + α + β + 1

\Rightarrow - \frac{1}{2} + \frac{7}{6} + 1

\Rightarrow \frac{- 3 + 7 + 6}{6}

\Rightarrow \frac{10}{6}

\Rightarrow \frac{5}{3}

So,

(α + 1) (β + 1) = \frac{5}{3} .

Hence, the correct option is 2.

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