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If and are the zeros of the polynomial f(x)=6x^2-3-7x, then

Question

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

\frac{5}{2}

\frac{5}{3}

\frac{2}{5}

\frac{3}{5}

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Noah Discussed

α

and

β

are the zeros of the polynomial

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

, then

(α + 1) (β + 1)

is equal to

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

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

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

α

β

are the zeros of the quadratic polynomial

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

, then

(α + β) = \frac{- b}{a} = - \frac{( - 7 )}{6} = \frac{7}{6}, α β = \frac{c}{a} = \frac{- 3}{6} = \frac{- 1}{2}

Now,

(α + 1) (β + 1)

= α β + α + β + 1

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

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

= \frac{10}{6}

= \frac{5}{3}

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Question Text	If $α$ and $β$ are the zeros of the polynomial $f (x) = 6 x^{2} - 3 - 7 x$ , then $(α + 1) (β + 1)$ is equal to
Answer Type	Text solution:1
Upvotes	150