Use graph of the function f(x)

[keerthivasanb]

1. Use graph of the function f(x) = x^2 to find how the number of roots of the equation depends on the value of b

x^2 = x - b

Answer the following -

if b < ___, the equation has 2 roots,
if b = ___, the equation has 1 root.
if b = ___, the equation has no roots

 

[ksdhart2]

Suppose we subtracted \(x\) from and added \(b\) to both sides, thus obtaining \(x^2 - x + b = 0\). This is a quadratic in terms of \(x\). What do you know about how the discriminant determines the number and types of roots a quadratic will have? Where does this lead you?

 

[Dr.Peterson]

Since they say to use the graph of y = x^2, I would guess what they want you to do is just draw a series of lines y = x - b, such as y = x, y = x - 1, y = x - 2, and so on; then think about which values of b produce 0, 1, and 2 intersections.

You'll have to use fractions, and graph accurately, and you may not be certain of your answer (as graphing is not exact), but you will gain a way to visualize such questions.

Let us know what you find.

 

[Steven G]

I hate these problems because you need to cheat! In my opinion you 1st need to use ksdhart2's method to find the exact answers, hide this work from your teacher, then use Dr Peterson's method, as this is what you were asked to use, to finish up the solution.

 

[keerthivasanb]

Thank you all for pointing me in the right direction.

I was able to solve the problem. Appreciate your help!