$Factorise the following by splitting the middle term and find the roots. 2 x^{2} + x - 6 = 0$

$x = 2 o r x = - \frac{3}{2}$

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$x = - 2 o r x = \frac{3}{2}$

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$x = - 2 o r x = - \frac{3}{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$x = 2 o r x = \frac{3}{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is B
$x = - 2 o r x = \frac{3}{2}$

$Given, 2 x^{2} + x - 6 = 0$

$2 x^{2} + x - 6 = 2 x^{2} + 4 x - 3 x - 6 = 2 x (x + 2) - 3 (x + 2) = (x + 2) (2 x - 3)$

$2 x^{2} + x - 6 = 0$
$\Rightarrow (x + 2) (2 x - 3) = 0$

$∴ x + 2 = 0 o r 2 x - 3 = 0 \Rightarrow x = - 2 o r x = \frac{3}{2}$

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