Real numbers??

[steven]

I do not know how to do this problem... how many real number solutions does the equation 7x^2 -5x+1=0 have?

 

[Deleted member 4993]

I do not know how to do this problem... how many real number solutions does the equation 7x^2 -5x+1=0 have?

That is a quadratic equation - what do you know about those?

 

[steven]

I think that they can be graphed as a function and that will tell me how many solutions it has 1, 2 or none... depending on how many times it crosses the x axis...

 

[Denis]

I think that they can be graphed as a function and that will tell me how many solutions it has 1, 2 or none... depending on how many times it crosses the x axis...

WHY do you "think" that? Are you attending math classes?

 

[mmm4444bot]

Plotting the function is one approach (graphical).

Evaluating the Discriminant to discover its sign is another approach (algebraic).

Have you learned about the Discriminant ? It is the radicand, in the Quadratic Formula (B^2 - 4AC).

Think about what happens, if the radical in that formula goes away. What's left is -B/(2A). That's a single number.

So, if the Discriminant is zero, there can be only one Real solution.

Tell me what happens, if the Discriminant is negative. What happens in the Real number system then?

If the Discriminant has a positive value, then we have two solutions because of the "plus or minus" part in the Quadratic Formula.

Does this make sense ?

You could read more in your textbook, by looking up "discriminant" in the book's index, followed by searching for information related to the sign of the discriminant.