Question

the function g(x) is defined as g(x) = 6x2 23x – 4. when does g(x) = 0? x = –6 or x = x = –4 or x = x = or x = 6 x = or x = 4

Answer 1

g(x) = 0 means 6x^2 + 23x – 4 = 0

6x^2 + 24x - x - 4 = 0
6x(x + 4) -1(x + 4) = 0
(6x - 1)(x + 4) = 0
x = 1/6 or x = -4

Answer 2

`x=1/6` or
`x=-4`

Explanation:

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`g(x)=6x^(2) +23x-4`

equate the function to zero

`6x^(2) +23x-4=0`

so

`a=6\\b=23\\c=-4`

substitute in the formula

`x=\frac{-23(+/-)\sqrt{23^(2)-4(6)(-4)}} {2(6)}`

`x=\frac{-23(+/-)√(529+96)} {12}`

`x=\frac{-23(+/-)25} {12}`

`x1=\frac{-23+25} {12}=1/6`

`x2=\frac{-23-25} {12}=-4`

The solution is
`x=1/6` or
`x=-4`