How do I find an equation that touches the x axis but does not pass through it?

Question

The equation cannot be solved quadratically. But the aim for the equation is to show that decimal search cannot work on the equation due to the fact that there is no change of sign but it is still a root. Any suggestions? Thanks

Answer 1

The idea is to write equations with analogous of these functions
y = 0
y = a x^2
y = a x^4 + b x^2
y = a x^6+b x^4 + c x^2
...

The y values are all of the same sign. 0 is a root. a, b, c are numbers.

Answer 2

1

Answer 3

I am not sure what you are looking for exactly, but assuming that you are working with a polynomial, any root of even multiplicity only touches the x-axis and doesn't pass through it. So you would need to know the multiplicity to know for sure. You can also use the Bisection Method to locate roots. (I am not sure if this notation is universal-but it is used in the book that I am teaching out of: Calc for Biology and Medicine by Claudia Neuhauser.) This method is an application of the intermediate value theorem and can be used if you are looking for a root when the function crosses the x-axis. Maybe you could modify the method through iterations on the computer to adjust for your situation. Hope this helps.

Answer 4

The equation y=0 touches but does not pass through the x-axis.

Answer 5

for this it has to meet x axis at 1 point only. if quadratic equation ax^2+bx+C. then use b^2-4ac=0

Answer 6

What's wrong with simply using y = x^2?

Answer 7

find the equation of the tangent

Answer 8

why not try y= (sinx)-1
{-infinity
the maximum for sinx is1,therefore,it will touch
the x-axis,but never go through it

i hope that this helps

Answer 9

Ah, but then you just differentiate it and voila!