Polynomials (1 Viewer)

[jaychouf4n]

ok

Find the equation to the curve y^3=x^2 at point P(t^2,t^3), hence, find where the tangent meets the curve again.

Ok is got the equation of the tangent and solved simultaneously with the equation of the curve, and got a cubic. So I know t^2 is one root of the equation, but in the back it says t^2 is a double root. Why is that??

N.B. I've done the question i just don't know why t^2 is a double root based on the information we know.

 

[lyounamu]

ok

Find the equation to the curve y^3=x^2 at point P(t^2,t^3), hence, find where the tangent meets the curve again.

Ok is got the equation of the tangent and solved simultaneously with the equation of the curve, and got a cubic. So I know t^2 is one root of the equation, but in the back it says t^2 is a double root. Why is that??

N.B. I've done the question i just don't know why t^2 is a double root based on the information we know.

Is your question correct?

 

[jaychouf4n]

yup terry lee 3.4 1b)

god i'm killing myself right now...can't even do q1

 

[jaychouf4n]

In the back it says

4x^3-9t^2x^2+6t^4x-t^6

This equation has 3 roots, two of which are t^2,t^2. Let the 3rd root be alpha etc

 

[lyounamu]

yup terry lee 3.4 1b)

god i'm killing myself right now...can't even do q1

Look at your first sentence of post 1.

It doesn't see right.


y^3 = x^2 with point (t^2, t^3)?

You mean y^3 = x^2 with point (t^3, t^2)?

 

[jaychouf4n]

oh crap whoops

y^2=x^3 P(t^2,t^3)

 

[lyounamu]

In the back it says

4x^3-9t^2x^2+6t^4x-t^6

This equation has 3 roots, two of which are t^2,t^2. Let the 3rd root be alpha etc

okie dokie

t^2 is a double root because if you look at it and differentiate it, you will see that t^2 is a zero for both non-derivative and first derivative one.

 

[Trebla]

ok

Find the equation to the curve y^3=x^2 at point P(t^2,t^3), hence, find where the tangent meets the curve again.

Ok is got the equation of the tangent and solved simultaneously with the equation of the curve, and got a cubic. So I know t^2 is one root of the equation, but in the back it says t^2 is a double root. Why is that??

N.B. I've done the question i just don't know why t^2 is a double root based on the information we know.

Note that t² is the x value of P(t², t³). Your equation to solve is a cubic. The tangent passes through only two points, so this implies that a double root exists (as it does not pass through 3 points but 2). Since the tangent "touches" x = t², then the double root exists at that value. If it wasn't a double root, the tangent would pass straight through that point.

 

[tommykins]

Look at your first sentence of post 1.

It doesn't see right.


y^3 = x^2 with point (t^2, t^3)?

You mean y^3 = x^2 with point (t^3, t^2)?

It's (t^2, t^3)

 

[lyounamu]

It's (t^2, t^3)

Well, in relation to the original question that he posted up, it should be (t^3, t^2) because he said that y^3 = x^2

 

[tommykins]

Well, in relation to the original question that he posted up, it should be (t^3, t^2) because he said that y^3 = x^2

Oh right I see. Gotcha (Y)