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If \alpha ,\beta are the roots of x^{2}-x+4=0 the the value of \left ( 2-\alpha \right )\left ( 2-\beta \right ) is

Option: 1

6


Option: 2

4


Option: 3

3


Option: 4

None of these


Answers (1)

best_answer

$$ \begin{aligned} &(2-\alpha)(2-\beta) \\ =& 4-2 \alpha-2 \beta+\alpha \beta \\ =& 4-2(\alpha+\beta)+\alpha \beta \end{aligned}       ---(1)

Now,\alpha+\beta=1, \alpha \beta=4

(Using sum and products of roots)

So,(2-\alpha)(2-\beta) \\

= 4-2(1)+4 \\

=6

Posted by

Sanket Gandhi

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