Max Magnitude of a,b,c in Quaratic Equation |ax^2+bx+c|<=1

  • Thread starter Thread starter ritwik06
  • Start date Start date
AI Thread Summary
The discussion focuses on finding the maximum magnitudes of the coefficients a, b, and c in the quadratic equation ax^2 + bx + c, constrained by the inequality |ax^2 + bx + c| ≤ 1 for all x in the interval [0, 1]. It is established that setting x=0 leads to the conclusion that |c| must be less than or equal to 1, giving a maximum magnitude of 1 for c. The conversation emphasizes that the coefficients a and b cannot be determined independently; instead, they are interrelated due to the nature of the quadratic function fitting within the defined bounds. The participants suggest considering the intersection points of the parabola with the bounding box to derive relationships among the coefficients. Overall, the discussion highlights the complexity of determining the coefficients under the given constraints.
ritwik06
Messages
577
Reaction score
0

Homework Statement



|ax^{2}+bx+c|\leq1 \forall x\in[0,1]
Find the maximum magnitude of a,b, and c possible!

My attempt:
putting x=0;
|c|<=1
hence its maximummagnitude is 1.
Help me with a and b.
regards,
Ritwik
 
Physics news on Phys.org
You aren't going to be able to set limits on the coefficients separately, I think. You are probably going to have relationships between the coefficients.

Picture it this way. The inequality is saying that

<br /> -1 \leq ax^{2}+bx+c \leq 1 for 0 \leq x \leq 1.

So a portion of the curve for this function has to fit entirely in the "box" bounded by x = 0, x = 1, y = -1, and y = 1. (Obviously, the parabola goes on forever elsewhere...) What does that mean for intersection points of the parabola with the "box"? How might you find coefficients from that?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

What Are the Values of A, B, and C for the Given Expression?
Replies
19
Views
2K
Conceptual question on equations of the form ##x=ay^2+by+c##
Replies
5
Views
1K
Solving these Simultaneous Equations
Replies
3
Views
2K
Find a and b to make this equation symmetric about the y-axis: y = ax^2 + bx^3
Replies
24
Views
3K
Got stuck due to the inequality not being satisfied
Replies
21
Views
3K
Is there a reason Lang uses (x-s)^2 instead of (x+s)^2?
Replies
4
Views
2K
Multiple in logarithm question -- find the variable?
Replies
16
Views
3K
Find the range of values of a + b
Replies
6
Views
1K
Prove a rational fraction is equal to another
Replies
5
Views
2K
The discriminant of a quadratic and real solutions
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top