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Factorisation of Quadratic Polynomials - Factor Theorem

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Question

Find the roots $2 x^{2} + x - 6 = 0$ by factorization.

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Solution

$2 x^{2} + 2 - 6 = 0$
$2 x^{2} + 4 x - 3 x - 6 = 0$
$2 x (x + 2) - 3 (x + 2) = 0$
$(2 x - 3) (x + 2) = 0$
$x = \frac{3}{2}, - 2$
$∴$ Roots are $\frac{3}{2}, - 2$

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