Questions on quadratic equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-h)^2+k$ or $y=a(bx+c)(cx+d)$.
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10answers
5k views
Why can ALL quadratic equations be solved by the quadratic formula?
In algebra, all quadratic problems can be solved by using the quadratic formula. I read a couple of books, and they told me only HOW and WHEN to use this formula, but they don't tell me WHY I can use ...
3
votes
5answers
284 views
How to “Re-write completing the square”: $x^2+x+1$
The exercise asks to "Re-write completing the square": $$x^2+x+1$$
The answer is: $$(x+\frac{1}{2})^2+\frac{3}{4}$$
I don't even understand what it means with "Re-write completing the square"..
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3
votes
4answers
156 views
Proving Quadratic Formula
purplemath.com explains the quadratic formula. I don't understand the third row in the "Derive the Quadratic Formula by solving $ax^2 + bx + c = 0$." section. How does $\dfrac{b}{2a}$ become ...
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votes
0answers
47 views
Sample Code to Generate Points on the Rim of a Randomly Rotated Cone : What's Going On Here?
Related to this question:
http://math.stackexchange.com/questions/407897/randomly-generate-point-on-shell-from-3-points-2-angles-with-uniform-angle-dis
I'm trying to reverse engineer the ...
3
votes
4answers
190 views
Where is the order of the variables inside the parentheses coming from?
I'm reading Sawyer's Prelude to Mathematics, here:
I can't understand what's the meaning and application of "condition" here. Also when he gives the example on the cubic equation, stating that ...
2
votes
1answer
39 views
How do I transform the equation based on this condition?
If a and b are the roots of the equation $$2x^2-px+7=0$$ Then a-b is a root of ?
5
votes
2answers
514 views
Solution af a system of 2 quadratic equations
I have a system of two quadratic equations with unknowns $x$ and $y$:
$$a_{1 1} x y + a_{1 2} x^2 + a_{1 3} y^2 + a_{1 4} x + a_{1 5} y + a_{1 6} = 0,\\
a_{2 1} x y + a_{2 2} x^2 + a_{2 3} y^2 + a_{2 ...
5
votes
2answers
348 views
Find equation of quadratic when given tangents?
I know the equations of 4 lines which are tangents to a quadratic:
$y=2x-10$
$y=x-4$
$y=-x-4$
$y=-2x-10$
If I know that all of these equations are tangents, how do I find the equation of the ...
3
votes
2answers
248 views
Integrating $\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x$
I've been trying to integrate this:
$$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$$
Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up ...
1
vote
1answer
44 views
What technique reduces factorable ax^2+bx+c=0 to factorable where a=1
The normal way to factor ax^2+bx+c=0 is to look for t,u,v,w such that:
(tx+u)(vx+w) = 0
so that tv=a, uw=c, and uv+wt=b.
This can be tricky, since there can be several possibilities for t,u,v,w. ...
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vote
3answers
153 views
How do I solve a Continued Fraction of solution to quadratic equation?
I know that it is possible to make a CF (continued fraction) for every number that is a solution of a quadratic equation but I don't know how.
The number I'd like to write as a CF is:
$$\frac{1 - ...
