Question

The sum of the roots of 8x² - 2x = 1 is:
A. -1/4
B. 1/4
C. -1/8

Answer 1

`8x^2-2x=1\implies8x^2-2x-1=0\implies x^2-\frac14x-\frac18=0`

The sum of the roots is
`\frac14`. By the fundamental theorem of algebra, a quadratic polynomial has 2 roots
`r_1,r_2` and can be written as

`(x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2`

so the sum of the roots is -1 times the coefficient of the degree 1 term.