Question

F(x)=2x-3g(x) =3x2 +3x+7Solve them as equations

Answer 1

1) Let's turn them as equations

f(x) = 2x -3 Make f(x) =0

2x -3 =0 Add 3 to both sides

2x = 3 Divide both sides by 2

x=3/2

This is the x-intercept of that function f(x) = 2x -3

As for g(x) = 3x²+3x +7

g(x) = 3x²+3x +7 Make g(x) =0

3x² +3x +7 =0

Let's solve it use the Resolutive Formula for Quadratic Equation

`\begin{gathered} \Delta=(3)^2-4(3)(7)\text{ }\Rightarrow\Delta=-75 \\ x=\frac{-3+-\sqrt[]{-75}}{2(3)} \\ x_1=-(1)/(2)+\frac{5\sqrt[]{3}i}{6} \\ x_2=-(1)/(2)-\frac{5\sqrt[]{3}i}{6} \end{gathered}`

So as we can see, the equation has complex roots and therefore the parabola does not intercept the x-axis in any point