If $α$ , $β$ are the roots of the equation $x^{2} - 5 x + 6 = 0$ , then the value of $α^{2} - β^{2}$ is:

\pm 5

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\pm 13

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\pm 6

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\pm 7

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Solution

The correct option is A $\pm 5$
The given quadratic equation $x^{2} - 5 x + 6 = 0$ can be factorised as:
$\Rightarrow x^{2} - 3 x - 2 x + 6 = 0$
$\Rightarrow x (x - 3) - 2 (x - 3) = 0$
$\Rightarrow (x - 3) (x - 2) = 0$
$\Rightarrow x = 3, 2$

If $α = 3$ and $β = 2$ , then $α^{2} - β^{2} = 9 - 4 = 5$
If $α = 2$ and $β = 3$ , then $α^{2} - β^{2} = 4 - 9 = - 5$

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