# Tagged Questions

A quadratic equation is of the form $ax^2 + bx + c = 0$, $a \neq 0$.

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Suppose I want to find the $n$ for which $$(n)(n+1)/2 = 10 \Longrightarrow n^2 + n - 20 = 0$$ Clearly a solution is $4$. But, suppose we wanted to find that solution by use of quadratic formula. ...
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### If someone has a velocity of $32$ ft/sec, will they be able to ring the bell( more info below)? [closed]

At a carnival, a new attraction allows contestants to jump off a springboard onto a platform to be launched vertically into the air. The object is to ring a bell located $20$ ft overhead. The ...
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### Why sometimes we get only one root of quadratic equations?

What is logic behind getting (sometimes) only one root of a quadratic equation which satisfies the equation?
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### How do you find out the range of values when dealing with simultaneous equations?

Find the range of value for $k$ for which $kx + y = 3$ meets $x^2 + y^2 = 5$ in two distinct points. im so stuck can someone give me a clear guide to the correct method and answer, thank you
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### Parametrization of $ax^2+bxy+c=0$

Can I just fix $y=t$ and use quadratic formula to get the rational points of the diophantine $$ax^2+bxy+c=0?$$ or is there another method? I feel like I am turning in circles with the quadratic ...
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I am confused with this question- if $ax^2+bx+c$ have no real roots then- $1+c/a+b/a$ is-- a. Positive b. Negative c. Zero d. Can.t say I tried attempting it as follows $b^2-4ac<0$ so ...
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Let $az^2+bz+c=0$ be a quadratic equation with complex coefficients $a,b,c$ and roots $z_1, z_2.$ If it is given that $|z_1|\not=|z_2|,$ how can I obtain the condition for this containing $a,b,c?$ ...
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### If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$ My Procedure The roots are $$\frac{-b+\sqrt{b^{2}-4ac}}{2a}$$ and ...
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I have an equation that looks like the following: $$A\cdot\mathrm{diag}(x)\cdot x + B\cdot x + c = 0$$ where $A, B, C \in \mathbb{R}^{n \times n}$ and $x, c \in \mathbb{R}^n$. $x$ is unknown. ...
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### List the elements of the set $\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$ [closed]

I don't get this maths equation Can anybody explain it ? Thanks List the elements of the following set: $A=\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$.
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### About diagonalizing a matrix for a quadratic expression (with the goal of uncoupling mixed terms)

my question is originated from a physical problem. I will try to present the problem as simple as possible, but I fear it will still be long since I'm bad at expressing myself briefly. It starts with ...
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### Solve system with different variables

I need to solve the system: $$x^2+2xy+y^2-1 = 0$$ where variable is $x$ AND $$x^2 + 2xy = 0$$ where variable is $y$. From the first Ι take discriminant, and end in one solution $x_1 = 1-y$ and ...
### In what base does the equation $x^2 - 11x + 22 = 0$ have solutions $6$ and $3$?
If we have below equation and know that $6$ and $3$ are answers of this equation, how to obtain the base used in the equation? $$x^2 - 11x + 22 = 0$$ Partial result The base is not $10$. (Because ...
### Manipulate the Physics Equation $P = I^2R$ to get R by itself
Given that $P = (V^2 R_1)/(R_1 + R_2)^2$, manipulate the equation so that we get $R_1$ by itself and that we have a quadratic equation. Where $V, P, R_1$, and $R_2$, are variables. I'm stuck when I ...