The given function g(x) = 4x² + 11x +6 is already in its general form in which the value of a = 4, b = 11, and c = 6. We will needing these values in the quadratic formula.
The formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Let's plug into the formula above the values of a, b, and c.
[tex]x=\frac{-11\pm\sqrt{11^2-4(4)(6)}}{2(4)}[/tex]
Then, solve.
a. Simplify the numbers inside the parenthesis.
[tex]x=\frac{-11\pm\sqrt{121-96}}{2(4)}\Rightarrow x=\frac{-11\pm\sqrt{25}}{2(4)}[/tex]
b. Get the square root of 25 and simplify the denominator.
[tex]x=\frac{-11\pm5}{8}[/tex]
c. Separate the plus and minus symbol and solve.
[tex]\begin{gathered} x=\frac{-11+5}{8}\Rightarrow x=\frac{-6}{8}\Rightarrow x=-\frac{3}{4} \\ x=\frac{-11-5}{8}\Rightarrow x=\frac{-16}{8}\Rightarrow x=-2 \end{gathered}[/tex]
The zeros and x-intercepts are the same. They are -3/4 and -2.
