Question

$\sqrt{3} {x}^{2} - 4x - 7 \sqrt{3} = 0$
Solve by Factorisation Method​

Answer 1

Concept Used:-

Splitting of middle terms :-

In order to factorize  x² + bx + c we have to find numbers p and q such that p + q = b and pq = c.

After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

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❥ Solution :-

$\tt \:  ⟼ \sqrt{3} {x}^{2} - 4x - 7 \sqrt{3} = 0$

$\tt \:  ⟼ \: \sqrt{3} {x}^{2} + 3x - 7x - 7 \sqrt{3} = 0$

$\tt \:  ⟼ \sqrt{3} {x}^{2} + \sqrt{3} \times \sqrt{3} x - 7x - 7 \sqrt{3} = 0$

$\tt \:  ⟼ \sqrt{3} x(x + \sqrt{3} ) - 7(x + \sqrt{3} ) = 0$

$\tt \:  ⟼(x + \sqrt{3)} ( \sqrt{3} x - 7) = 0$

$\tt\implies \:x = - \sqrt{3} \: or \: x = \dfrac{7}{ \sqrt{3} }$

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