Solve by factorisation method √3x² -2√2x - 2√3 = 0

1.	Solve by factorisation method √3x² -2√2x - 2√3 = 0
Answer» ANSWER: • Factorised FORM : $(\sqrt{3}x+ \sqrt{2}) (x - \sqrt{6})$ • ROOTS : $\dfrac{- \sqrt{2}}{\sqrt{3}} \; and \; \sqrt{6}$ Step-by-step EXPLANATION: $\sqrt{3}x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0$ $\implies \sqrt{3}x^2 -3\sqrt{2}x + \sqrt{2}x - 2\sqrt{3} = 0$ $\implies \sqrt{3}x(x - \sqrt{3}\sqrt{2}) +\sqrt{2}(x - \sqrt{3}\sqrt{2}) = 0$ $\implies \sqrt{3}x(x - \sqrt{6}) + \sqrt{2}(x - \sqrt{6}) = 0$ $\implies (\sqrt{3}x+ \sqrt{2}) (x - \sqrt{6}) = 0$ $\\$ Finding the roots now ! $(i) (\sqrt{3}x+ \sqrt{2}) = 0$ $\implies \sqrt{3}x = -\sqrt{2}$ $\implies x = \dfrac{- \sqrt{2}}{\sqrt{3}}$ $\\$ $(ii) (x - \sqrt{6}) = 0$ $\implies x = \sqrt{6}$ $\\$ • Factorised Form : $(\sqrt{3}x+ \sqrt{2}) (x - \sqrt{6})$ • Roots : $\dfrac{- \sqrt{2}}{\sqrt{3}} \; and \; \sqrt{6}$ $\\$ THANKS !

Answer»