If $α$ and $β$ are the roots of the equation $x^{2} - 3 x + 2 = 0$ , form a equation whose roots are of $- α$ and $- β$ .

x^{2} + 3 x + 2 = 0

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x^{2} - 3 x + 2 = 0

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x^{2} + 3 x - 2 = 0

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None of these

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Solution

The correct option is A $x^{2} + 3 x + 2 = 0$
$\Rightarrow$ $α$ and $β$ are the roots of the equation $x^{2} - 3 x + 2 = 0$
$\Rightarrow$ $x^{2} - 3 x + 2 = 0$
$\Rightarrow$ $x^{2} - 2 x - x + 2 = 0$
$\Rightarrow$ $x (x - 2) - 1 (x - 2) = 0$
$\Rightarrow$ $(x - 2) (x - 1) = 0$
$\Rightarrow$ $x = 2$ and $x = 1$
$∴$ $α = 2$ and $β = 1$
$\Rightarrow$ The new roots are $- α$ and $- β$ , the the roots become $- 2$ and $- 1$
$\Rightarrow$ Sum of the roots $= - 2 + (- 1) = - 3$ ---- ( 1 )
$\Rightarrow$ Product of the roots $= (- 2) \times (- 1) = 2$ ----- ( 2 )
$\Rightarrow$ $x^{2} - (S u m o f t h e r o o t s) x + (P r o d u c t o f t h e r o o t s) = 0$
$\Rightarrow$ $x^{2} - (- 3) x + 2 = 0$
$\Rightarrow$ $x^{2} + 3 x + 2 = 0$

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