Question

Factorise X2-2root3x-24

Answer 1

x² - 2√3x - 24
we should split 2√3 in such a what that product of each components of 2√3 must be equals -24 .
so, let's try .
2√3 can be written (4√3 - 2√3)
And also 4√3 × -2√3 = -4 × 2 × 3 = -24
∴ x² - 2√3x - 24
= x² - (4√3 - 2√3)x - 24
= x² - 4√3x + 2√3x - 24
= x(x - 4√3) + 2√3(x - 4√3)
= (x + 2√3)(x - 4√3)

Hence, factorisation of x² - 2√3x - 24 = (x + 2√3)(x - 4√3)