i dont have the asnwer to this polynomial q, what is it (1 Viewer)

[yashbb]

 

[A1La5]

Using DESMOS the point G is . The other intersection point of the two graphs is not valid in this case as at this point the graph of cuts through the graph of (In layman terms a tangent is a line that just touches a curve at one point, rather than slicing through it). At the point the tangent line just touches the graph of , which matches the definition of what a tangent is.

In an exam situation it would be best to draw both of the graphs and to then determine which of the two intersection points is the right one.

 

[CM_Tutor]

In an exam, you would be expected to say that the condition for the tangent to meet the curve is

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This cubic equation must have three roots, but because the line is a tangent to the curve, the -coordinate of that point (and hence the corresponding solution to the cubic) must be a double root. Thus, let the cubic equation have roots and apply root theory to deduce that and .

 

[yashbb]

In an exam, you would be expected to say that the condition for the tangent to meet the curve is

​

This cubic equation must have three roots, but because the line is a tangent to the curve, the -coordinate of that point (and hence the corresponding solution to the cubic) must be a double root. Thus, let the cubic equation have roots and apply root theory to deduce that and .

yep got it correct thank you so muchhhhh