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If , $β$ be the zeroes of the quadratic polynomial $2 x^{2} + 5 x + 1$ , then the value of $α + β + αβ =$

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-2

-1

None of these

answer is A.

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Detailed Solution

Given, ,

β

be the zeroes of the quadratic polynomial

2 x^{2} + 5 x + 1 .

We need to find the value of

α + β + αβ .

Taking the equation

a x^{2} + bx + c = 0

.
We know that,
Sum of roots

= \frac{- b}{a}

Product of roots

= \frac{c}{a}

Assume that

α

and

β

are the quadratic equation's zeroes.
Therefore,

α + β = - \frac{5}{2}

αβ = \frac{1}{2}

Now,

α + β + αβ = - \frac{5}{2} + \frac{1}{2}

\Rightarrow - \frac{4}{2}

\Rightarrow - 2

Hence,

α + β + αβ = - 2 .

Hence, the correct option is 1.

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