Question

Factorisation of: $2x^2-\frac{5}{6}x+\frac{1}{12}$ is $2(x+\frac{1}{a})(x+\frac{1}{b})$. Find $-a-b$.

Answer 1

$2x^2-\frac{5}{6}x+\frac{1}{12}=2(x^2-\frac{5}{12}x+\frac{1}{24})=2(x^2-\frac{3x}{12}-\frac{2x}{12}+\frac{1}{24})=2(x-\frac{1}{4})(x-\frac{1}{6})=2(x+\frac{1}{-4})(x+\frac{1}{-6})$

Hence, $a+b=-4+-6=-10$