# Tagged Questions

Questions on quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

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Question: A ball is dropped from a height of $18$ metres. The quadratic equation $h = -2t^2 + 18$ gives you the height, $h$ metres, of the ball, after $t$ seconds. After how many seconds does the ...
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### Show that $2\cosh z + \sinh z = i$

The equation is $$2\cosh z + \sinh z = i$$ I used the following formulas: $$\cosh z = \frac{e^z + e^{-z}}{2}, \sinh z = \frac{e^z - e^{-z}}{2}$$ to reduce this equation to $$3e^z - e^{-z} = 2i$$ but ...
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### The equation $x^2+ax+(b+2)=0$ has real roots. Find the minimum value of $a^2+b^2$. [closed]

The equation $x^2+ax+(b+2)=0$ has real roots. Find the minimum value of $a^2+b^2$.
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### Center and axis of Quadratic Surface

Given a Quadratic Surface in the form: $ax^2+by^2+cz^2+2fyz+2gzx+2hxy+2px+2qy+2rz+d=0$ I know how to decide which kind of surface is represented (http://mathworld.wolfram.com/QuadraticSurface.html). ...
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If c is a real number and the negative of one of the solutions of $x^2 -3x +c=0$ is a solution of $x^2 +3x -c=0$ then the solution of $x^2-3x+c=0$ are.... i cant do this problem due to language ...
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### Solving a logarithmic equation where the logarhitm is exponentiated

I have troubles solving the following logarthitmic equation. $$\ 2(\log_x{\sqrt7})^2-\log_x{\sqrt7}-1 =0$$ The results are supposed to be $\ x_1 = {\frac{1}{7}}, x_2 = \sqrt7$ I have tried ...
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### How to solve quadratic equation in 4 variables?

I am trying to solve the equation $a^2 + b^2 + c^2 + d^2 = \alpha$ where alpha is a constant and $a, b, c$, and $d$ are the $4$ variables. I need to find some integer values of $a, b, c$ and $d$ which ...
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### Finding the intersection between a plane and an ellipsoid

I have an ellipsoid (That can be rotated), described by its conic equation : $$E : a_1x² + a_2y² + a_3z² + 2a_4xy + 2a_5xz + 2a_6yz + a_7x + a_8y + a_9z + \gamma = 0$$ This ellipsoid can be ...
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### Testing if a Point is inside an oriented ellipsoid

So my goal is to do a search for the points that are inside an ellipsoid. for that i need to test if each point is inside. I need to be able to orient my ellipsoid, so i looked up how to write a ...
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### Can't find my mistake

I'm trying to find the sum of the reciprocal numbers of squares of quadratic equation:$3x^2-14x+6=0$, I managed to find the answer by calculating the roots, and summing their reciprocal. However ...
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### Equations $ax^2+btx+c=0, bx^2+ctx+a=0$ and $cx^2+atx+b=0$

Find different real numbers $a,b,c,t$ for which the following conditions: 1) the equation $ax^2+btx+c=0$ has real roots $x_1,x_2$; 2) the equation $bx^2+ctx+a=0$ has real roots $x_2,x_3$; ...
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### Determine a, b & c in a (possible) Quadratic equation [closed]

given f(x)=x: 1 - f(5)=2 2 - f(3)=3 how to determine the coefficients a, b & c in the polynomial equation like: ...