Mathematics Stack Exchange
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Questions tagged [quadratics]

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

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

The root of $y=ax^2+bx+c$ can be solved by the formula $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

5400 questions
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Help in understanding quadratic equation

Sorry if this is a complete dummy question, but I haven't done math in years and I'm quite rusty. I'm reading this explanation of least squares regression, which internally uses the quadratic equation solution. I was wondering if someone can tell me…
Hamy
  • 123
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Find length (requires quadratic equation)

There is an equation $l = 4\sqrt{(\frac{w^2+d^2}{4})+(h-k)^2}$ Following values are given $l = 50$ $w = 12$ $d = 10$ $k = 3$ What is $h$? Following choices are $14$ $10$ $11$ $12$ $13$ My answers come nothing near these! Here is what I am doing,…
Marium
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Why is the $2a$ term in the quadratic formula $|2a|$?

I am reading through Algebra by Gelfand/Shen. There was a construction of the quadratic formula as follows: $ax^2 + bx + c = 0$. Dividing by $a$ gives us $x^2 + \frac{b}{a}x + \frac{c}{a} = 0$ and we can apply the formula of the equation $x^2 + px…
user88528
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Range of rational function

How to find the Range of function $$f(x)= \frac{x^2+2x-3}{x^2 - 3x +2}$$ I made a quadratic equation in terms of y which came to be: $$ y(x^2 - 3x +2)= x^2+2x-3 $$ $$\implies x^2(y-1)-x(3y+2)+2y+3=0$$ Now I made two cases : When y=1 This means the…
Scáthach
  • 243
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Solving quadratic equation $x^2-(k+1)x+k+1=0$ using quadratic formula

Disclaimer I am new here so please mind how i have executed this question. Feel free to comment on how to improve as i have read on “how to ask a good question”. Problem I am having trouble answering this quadratic equation that my teacher at…
Sophia Serrato
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For what integral values of $a$ does $x^2-x(1-a) - (a+2)=0$ have integral roots?

For what integral values of $a$ does the equation $$x^2-x(1-a) - (a+2)=0$$ have integral roots? I have tried making the discriminant to be a perfect square; but when it becomes perfect square, $a$ itself is not an integer.
user587196
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Find (a,b,c) if $ax^2-bx+c=0$ have roots lying in $(0,1)$ where $a,b,c\in\mathbb{Z_+}$

Let the equation $ax^2-bx+c=0$ have distinct real roots both lying in the open interval $(0,1)$ where $a,b,c$ are given to be positive integers. Then the value of the ordered triplet $(a,b,c)$ can be $$ a)\quad (5,3,1)\;,\quad…
Sooraj S
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If $\alpha$, $\beta$ are the roots of the equation $ax^2 + 3x + 2 = 0,\; a<0$

Show that if $\alpha$, $\beta$ are the roots of the equation $ax^2 + 3x + 2 = 0,\; a<0$, then $$\dfrac{(\alpha^2)}{(\beta)}+\dfrac{(\beta^2)}{(\alpha)}> 0$$ I could only figure out two things first, that $a = \frac{-(3\alpha + 2)}{(\alpha^2)}$…
Virad Gupta
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Function with 2 unknowns and one needs to be solved

I have a homework question stating: Find the set of values of $k$ for which $f(x)=3x^2-5x-k>1$ for all $x\in\mathbb R$. This question has really confused me because I looked at the answer and the value of $k$ is meant to be $k<-\frac{37}{12}$ and…
Mason Kennedy
  • 23
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Quadratic Equation relation between roots

If the ratio of the roots of the equation $x^2+px+q=0$ are equal to the ratio of the roots of the equation $x^2+bx+c=0$ , then prove that $p^2c=b^2q$ Let $\alpha \& \beta$ be the roots of first equation then $\alpha + \beta = -p \& \alpha \beta = q$…
Sachin Sharmaa
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If the equations $ax^3+(a+b)x^2+(b+c)x+c=0$ and $2x^3+x^2+2x-5=0$ have a common root,then $a+b+c$ can be equal to

If the equations $ax^3+(a+b)x^2+(b+c)x+c=0$ and $2x^3+x^2+2x-5=0$ have a common root, then $a+b+c$ can be equal to(where $a,b,c\in R,a\ne0$) $(1)\;5a$ $(2)\;3b$ $(3)\;2c$ $(4)\;0$ As $x=1$ is the root of the equation $2x^3+x^2+2x-5=0$ and its other…
user984325
  • 651
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How can I find the equation of one parabola given the equation of another parabola?

The equation of the other parabola has to follow the form: $4p(x – h) = (y – k)^2$ because it is a sideways parabola. I can see that the vertex is at (-4.5,18) So then the equation would be $4p(x+4.5) = (y-18)^2$ Now I can just plug in a value like…
user477465
  • 720
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Quadratic Drawing

I was wondering if anyone could help me with the shading This is the picture: Here are my equations so far: I was wondering if anyone knew what domain and range constraints I could add to make only the inside of the petal shaded. Thanks
mjj
  • 111
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Finding a quadratic equation using roots

If $x_1$ and $x_2$ are the roots of $$ax^2+bx+c=0$$ then $x_1^3$ and $x_2^3$ are the roots of which equation? So I tried by solving this for $x_{1/2}$ so I could change it in $(x-x_1^3)(x-x_2^3)$ $x_{1/2}=\large{-b\pm{\sqrt{4ac}}\over2a}$ and…
Aleksa
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Find $k$ such that $2x^2 + 5x + k = 0$ has equal roots

Anyone have a method for solving this? The equation $2x^2 + 5x + k = 0$ has equal roots. Find the value of $k$.
Gabriel
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