polynomial question (1 Viewer)

[wgy182]

Hey

Polynomial question
Given that two of the roots of x^4+3x^3-7x^2-27x-18=0 have the same modulus but different signs, solve the equation. (hint- let two of the roots be (alpha) and -(alpha) and use the technique of equating coefficients.)

I am stuck on solving these type of questions.


Thanks in adVance

 

[Makematics]

Hey

Polynomial question
Given that two of the roots of x^4+3x^3-7x^2-27x-18=0 have the same modulus but different signs, solve the equation. (hint- let two of the roots be (alpha) and -(alpha) and use the technique of equating coefficients.)

I am stuck on solving these type of questions.


Thanks in adVance

voila

 

[wgy182]

Thankyou so much

 

[wgy182]

How do I find the smallest distance between the graphs of y=x^2-4x+12 and y=2x+1?

 

[asianese]

Take the difference of the two:

and then minimise d.

 

[wgy182]

Not sure what u mean by minimise the d

 

[asianese]

So d represents the distance between the curves. If you want to find the minimum distance, then you must find where the curve d(x) has a minimum turning point.

 

[wgy182]

Thanks but the answers in the book says it's 2sqrt5/5? So is the book's answer wrong?

 

[wgy182]

Also how do I simplify this: (25^n-5^n)/(5^(2n-1)-5^(n-1))

 

[RealiseNothing]

Thanks but the answers in the book says it's 2sqrt5/5? So is the book's answer wrong?

The answers in the book is right.

 

[RealiseNothing]

How do I find the smallest distance between the graphs of y=x^2-4x+12 and y=2x+1?

The minimum distance between the two graphs will be the perpendicular distance between the line, and the point on the parabola when the tangent to the parabola is parallel to the line

This is because the perpendicular distance from any point on the tangent to the line is the same as they are parallel. And since the tangent is in between both the line and the parabola, then when the line is parallel it will give the minimum distance:

As you an see, when it is parallel, the red and blue perpendicular lines are all the same distance, and hence it is obvious that the red line is the minimum distance between the parabola and the line.

So we find when the tangent is parallel, that is, when the gradient of the line is equal to the gradient of the parabola. The gradient of the line is just 2 since it is in the form . Now to find the gradient of the parabola and let it equal 2:









Sub this back into the parabola:



Thus at the point on the parabola, the tangent is parallel.

Now we find the perpendicular distance between the point and the line which is

 

[asianese]

Of course, the perpendicular distance is always the shortest distance (in a euclidean plane)!