Answer:
C. 3x + 8
Step-by-step explanation:
We have the quadratic expression [tex]12x^2+29x-8[/tex].
Equating the expression to 0, we get the equation, [tex]12x^2+29x-8=0[/tex].
Now, we know the solution of the quadratic equation [tex]ax^2+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{x^{2}-4ac}}{2a}[/tex]
As, we have,
a= 12, b= 29 and c= -8.
The solution is given by,
[tex]x=\frac{-29\pm \sqrt{29^{2}-4\times 12\times (-8)}}{2\times 12}[/tex]
i.e. [tex]x=\frac{-29\pm \sqrt{841+384}}{24}[/tex]
i.e. [tex]x=\frac{-29\pm \sqrt{1225}}{24}[/tex]
i.e. [tex]x=\frac{-29\pm 35}{24}[/tex]
i.e. [tex]x=\frac{-29+35}}{24}[/tex] and [tex]x=\frac{-29-35}{24}[/tex]
i.e. [tex]x=\frac{6}}{24}[/tex] and [tex]x=\frac{-64}{24}[/tex]
i.e. [tex]x=\frac{1}}{4}[/tex] and [tex]x=\frac{-8}{3}[/tex]
So, the factors of the expression [tex]12x^2+29x-8[/tex] are (4x-1) and (3x+8).
Thus, according to the options, the expression which is factor of the given equation is 3x + 8.
