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If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - x - 4$ find the value of $\frac{1}{α} + \frac{1}{β} - αβ$ .

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\frac{15}{4}

\frac{- 15}{4}

\frac{5}{4}

\frac{- 5}{4}

answer is A.

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Detailed Solution

Given, the quadratic polynomial

f (x) = x^{2} - x - 4

Now the standard quadratic polynomial can be given as,

f (x) = a x^{2} + bx + c

Now sum of roots for this equation

α + β = - \frac{b}{a}

So, for our equation,

α + β = - \frac{(- 1)}{1}

α + β = 1

Product of roots,

αβ

=c/a
So, for our equation,

αβ = \frac{(- 4)}{1}

αβ = - 4

Thus,

\frac{1}{α} + \frac{1}{β} - αβ

= \frac{α + β}{αβ} - αβ

= \frac{1}{- 4} - (- 4)

= \frac{- 1}{4} + 4

= \frac{15}{4}

Correct option is 1.

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