Question

A function g(x) has x-intercepts at (StartFraction 1 Over 2 EndFraction, 0) and (6, 0). Which could be g(x)? g(x) = 2(x + 1)(x + 6) g(x) = (x – 6)(2x – 1) g(x) = 2(x – 2)(x – 6) g(x) = (x + 6)(x + 2)

Answer 1

b

Explanation:

Answer 2

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

Explanation:

`g(x)` intercepts the x-axis at these 2 points:

`(6,0) ;(1/2,0)`

⇒ 6 and 1/2 are roots ie; if you insert
`x=6` or
`x=1/2` into the equation of g(x) you will obtain a 0.

`g(6) = g(1/2) = 0`

now in order for 0 to appear we should have
`x-6`

now in order for 0 to appear we should have
`x-1/2`

but
`x-1/2` doesn't appear in any of these, but its multiple of 2 is there:

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

Therefore the function;

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