0
votes
4answers
75 views

Find $\frac{a^3}{a^6 + 1}$ given a is a root of a quadratic equation

My question is: If a is a root of the equation $x^2 - 3x + 1 = 0$, then find the value of $\frac{a^3}{a^6 + 1}$. So, I figured we can use the Sridharacharya ...
0
votes
3answers
72 views

Additional solutions to quadratic equations which don't match the formula answer.

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 ...
0
votes
1answer
64 views

How do i solve this square root to solve for $y$ and get rid of $x$ at the same time

This is what I have and I don't know how to solve for $y$. Because $x$ is a variable it would be great if it would cancel out. $$ y = \frac{\sqrt{2.25^2Ax^2 + 2.25 \cdot2Bx}}{\sqrt{Ax^2 + 2Bx}} = ...
0
votes
0answers
150 views

what is the maximum number of roots of quadratic function with 3 variables?

Given the general quadratic form with 3 variables $(x,y,z)$: $ax^2 + by^2 +cz^2 + dxy + eyz +fzx + gx + hy + iz = 0$ satisfies $x^2 + y^2 + z^2 = 1$ I would like to ask what is the maximum number of ...
1
vote
1answer
58 views

Quadratic Equation - What am I doing wrong?

For which value of $c$ does the quadratic equation $5x^2 - 6x + c = 0$ have exactly one solution in terms of $x$? The solution is supposed to be $c = 1.8$, but I only ever get $c = 1$ ...
3
votes
4answers
203 views

Quadratic vertex form - negative $h$ means it's on the right side of the graph?

When putting a quadratic equation in vertex form, I am having difficulty understanding why $h$ is negative when the location of the parabola goes to the right... why is this? For example, if I ...
1
vote
1answer
212 views

Finding the minimum value of a quadratic within a range

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 ...