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?

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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
You do not need to look at the complete quadratic formula, just the discriminant b2-4ac. Do you know the condition on the discriminant for the equation to have (i)two real roots; (ii) one real repeated root; (iii) no real roots (equivalent to saying the equation has complex roots)?

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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
Yes, but that is before you take into account the 3 subtasks. If a graph touches the x-axis once, how does that affect the number of real solutions to the equation?

ooooooook so...
1. b=square root of 40
2 b is greater than square root of 40
3. b is less than square root of 40

is that right?