1. A quadratic fraction is of the form f(x)= 2x^2+bx+5
Find the values for b where the graph of f(x):
1.just touches the x-axis
2. has two x-intercepts
3.does not cut or touch the x-axis

I've tried using the quadratic formula but i have no idea how to do it when there are two unknowns. For number one i thought it must be when y=0 and i've tried substituting other numbers in but other than that i can't start. Can you please start me off?

When you apply the quadatic formula what are you getting? If $$x_{12} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ then what does it mean if $$x_{12}$$ is complex? What about if $$x_{12}$$ is real? What condition yields a $$x_{12}$$ as complex? and which condition yields $$x_{12}$$ as real?

b has to be a real number but how can you work it out when there are two unknowns .. x is unknown and so is b

danago
Gold Member
Using the quadratic formula FrogPad posted, pay special attention to the $$b^2-4ac$$ part.

cristo
Staff Emeritus