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

Answer:

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

Step-by-step 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

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

$x=\frac{-23(+/-)\sqrt{529+96}} {12}$

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

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

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

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