Question

A function g(x) has x-intercepts at (1/2,0) and (6,0). What could be g(x))?

Answer 1

g(x) = x² -
`(13)/(2)` x + 3 is a possible polynomial

given x -intercepts x = a and x = b, then

(x - a) and (x - b) are the factors and g(x) is the product of the factors

here x =
`(1)/(2)` and x = 6 are the x-intercepts, hence

(x -
`(1)/(2)`) and (x - 6) are the factors

g(x) = (x -
`(1)/(2)`)(x - 6)

= x² -
`(13)/(2)` x + 3