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Question

A quadratic equation with integral coefficient has two different prime numbers as its roots if the sum of the coefficients of the equation is prime, then the sum of the roots is


A
2
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B
5
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C
7
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D
11
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Solution

The correct option is B $$5$$
Let equation is $$k(x-\alpha) (x-\beta)=0$$  where $$ \alpha, \beta$$
are prime numbers.
Sum of coefficents $$= k+ k(\alpha+\beta)+k\alpha\beta=k(\alpha-1)(\beta-1)$$ 
$$\Rightarrow k=1$$ and one of $$(\alpha-1) $$and$$ (\beta-1)$$ will be one.
Let $$\alpha-1=1\Rightarrow \alpha=2$$
$$ \beta-1$$ will be 2.
So, $$\beta=3$$
Hence, sum of roots $$= 5$$.

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