Question

Find the x-intercept of the function g(x)=8x²-10x-3

Answer 1

To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.

We have the following:

`\begin{gathered} g(x)=8x^2-10x-3 \\ if\text{ g(x)=0} \\ \Rightarrow8x^2-10x-3=0 \end{gathered}`

we can use the quadratic formula to get the roots of the polynomial:

`\begin{gathered} a=8 \\ b=-10 \\ c=-3 \\ x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x_(1,2)=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(8)(-3)}}{2(8)}=\frac{10\pm\sqrt[]{196}}{16} \\ \Rightarrow x_(1.2)=(10\pm14)/(16) \\ \Rightarrow x_1=(10+14)/(16)=(24)/(16)=(3)/(4) \\ \Rightarrow x_2=(10-14)/(16)=(-4)/(16)=-(1)/(4) \end{gathered}`

therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)