Question

Factorise: 6x^2 - 5x^2 - √3 x + 12

Answer 1

Answer:

$(x-\frac{\sqrt3+3\sqrt{5}i}{2})(x-\frac{\sqrt3-3\sqrt{5}i}{2})$

Step-by-step explanation:

$6x^2 - 5x^2 - \sqrt3 x + 12\\=x^2-\sqrt3x+12\\\\\text{using quadratic formula,}\\x=\frac{\sqrt3\pm\sqrt{3-4\times12}}{2}\\x=\frac{\sqrt3\pm\sqrt{3-48}}{2}\\x=\frac{\sqrt3\pm\sqrt{-45}}{2}\\x=\frac{\sqrt3\pm3\sqrt{5}i}{2}\\\\\therefore x^2-\sqrt3x+12=(x-\frac{\sqrt3+3\sqrt{5}i}{2})(x-\frac{\sqrt3-3\sqrt{5}i}{2})$