# Tagged Questions

32 views

### Finding intersection points of 2 functions. My method is incomplete.

These are the 2 functions : $y = x^{4}-2x^{2}+1$ $y = 1-x^{2}$ Here's how I solved It : $x^{4}-2x^{2}+1 = 1-x^{2}$ $x^{4}-x^{2} = 0$ $x^2(x^2-1)=0$ $x^2-1=0$ $x=\pm \sqrt{1}$ Value of $y$ when ...
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### Signature of quadratic form $Q(p)=p(1)p(2)+p(3)p(4)$

I was asked to find the signature of the quadtratic form $Q(p)=p(1)p(2)+p(3)p(4)$ where $p$ is a polynomial in $\mathbb R_n[x]$ I tried doing it via finding the symmetric matrix that $Q$ corresponds ...
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I'm hoping for link to some resource which can explain why the following is true. $$x^2 + 104x - 896 = 0$$ Using the quadratic formula we pull a = 1, b = 104, c = 896. Putting that into the ...
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### solving for one variable in terms of others

A question from Steward's Precalculus textbook 5th, Pg 55, the original formula is $$h=\frac{1}{2}gt^2+V_0t$$ the question asks to write the formula in terms of $t$, the answer is ...
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I've performed LS fit to data in order to fit the following quadratic function: $$f(x,y) = A~x^2 + B~y^2 + C~x~y + D~x+E~y +F$$ Now, I would like to check that the fitted function looks like a ...
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### Find $a$ and $b$ in the given cubic polynomial

Find $a$ and $b$ such that $x+1$ and $x+2$ are factors of the polynomials $x^3+ax^2-bx+10$. Here I am not sure that how can I obtain the value of $a$ and $b$, I tried to multiply $x+1$ and $x+2$ to ...
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Find the Quadratic Equation whose roots are $2+\sqrt3$ and $2-\sqrt3$. Some basics: The general form of a Quadratic Equation is $ax^2+bx+c=0$ In Quadratic Equation, $ax^2+bx+c=0$, if ...
### Partitioning polynomials in $\mathbb{Z}[x,y]$ by the primes they represent
Suppose you have a set $S\subset\mathbb{Z}[x,y].$ How can one efficiently partition the polynomials into sets such that the primes represented by the polynomials in any given set are identical? For ...
Given any quadratic equation of the form $y=ax^2+bx+c$, I want to find the minimum value for a specific range of $x$. My programmer brain can do it in a branchy, algorithmic way as follows, but is ...