Mathematics Stack Exchange
Mathematics Stack Exchange

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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How do I factor this quadratic?

I'm going through the AoPS Algebra book, and I'm on the quadratics section. I'm given this challenge question: $ \displaystyle 2x^2 + 7x(\sqrt{3}) + 9 = 0$ And I have to solve for all values of $x$. How I try to do it: Simplify…
user164403
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Quadratic equations ..

The set of non-zero values of k such that the equation $|x^2-10x+9| =kx$ is satisfied by atleast one and atmost three values of x, lies in ___. The answer is $(-\infty, -16] \cup [4 , \infty) $. How do you get that ?
Mysterious
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can i solve this quadratic equation this way

I was basically doing a physics problem and came across this equation in midway $\dfrac{2n-1}{n^2} = \dfrac{11}{36}$ then I equated $2n-1 = 11$ and $n^2 = 36$ and the value of $n$ which I got is $6$ in both the cases is this method valid? I mean I…
agha rehan abbas
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Find the real parameter a so that the equation has real and positive roots

My problem is: $(2-x)(x+1)=a$ How do I find the value of the parameter $a$ so that the equation has real and positive roots?
Thunder
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How to solve a quadratic equation with two unknowns?

I know how to solve quadratic equations when there's only one unknown, but I'm a bit confused on what I do if I have $2$ unknowns e.g: $$x^2 + 2kx + 81 =0$$ With just $x^2 + 2kx + c=0$, obviously $x=-k \pm \sqrt{k^2 -c}$. I tried substituting the…
83457
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Find all prime $p$ such that the equation $x^2+px-330p=0$ has exactly one positive integral root.

From the equation the two factors of $-330p$ add up to $p$. But I wasn't able to set up a equation based the conditions given.
Valkyrie
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Quadratic equation cancellation error.

$$(x-1)^2 + 2x - 2 = (x+1)(x+2)$$ $$(x-1)^2 + 2(x-1) = (x+1) (x+2)$$ $$(x-1) (x-1+2) = (x+1) (x+2)$$ $$(x-1)\require{cancel}\cancel{(x+1)} = \require{cancel}\cancel{(x+1)}(x+2)$$ $$(x-1) = (x+2)$$ $$x-x = 2+1$$ $$0 = 3$$ But when i do it like…
Shaadi Alfred
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Find the range of values of $k$ for which the following equation has real roots.

Find the range of values of $k$ for which the following equation $x^2+(1-k)x=k$ has real roots. I tried it, for real roots, $b^2-4ac \geqslant 0$ $x^2+(1-k)x-k=0$ $(1-k)^2-4*1*(-k)\geqslant0$ ${(1)^2-2\cdot1\cdot…
Kiara
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Help an artist find an equation for the price of paintings of different sizes.

I'm an artist. I'm trying to find a way to calculate the price of paintings of varying sizes. I have tried to come up with some kind of equation to vary the price based on square cm. The thing is, you cannot have a fixed price per cm2 for paintings,…
Perceptor
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Quadratic Equations - Mixed Roots

This is probably a silly question but why is it that when a quadratic equation has a single root it must be a repeated root. Why can't the second root be an imaginary root?
asdf
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Pythagoras numbers and fermats last theorem

I am reading "What Is Mathematics? An Elementary Approach to Ideas and Methods" And I am stuck here, I don't get it. I have posted a screen shot underlining what my doubt is.. I dont get it when the author says while the pythagoras theorem is : $a^2…
Mihir Solanki
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Proving the minimum value of (x+a)(x+b)/(x+c)

Show that the minimum value of $\frac {(x+a)(x+b)}{(x+c)}$, where a$\gt$c, b$\gt$c, is $(\sqrt{a-c}+\sqrt{b-c})^{2}$ for real values of x$\gt-c$. I did $$\frac {(x+a)(x+b)}{(x+c)}=y$$ and then took its discriminant greater than zero. This led me to…
Tejas
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Find the coordinates of intersection of a line and a circle

There is a circle with a radius of $25$ ft and origin at $(0, 0)$ and a line segment from (0, -31) to (-37, 8). Find the intersections of the line and circle. I am asking for somebody to analyze what I am doing wrong in calculating the answer,…
kettlecrab
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Solving a simple equation, avoiding a quadratic

Sorry for the trivial question. I was wondering if there was an easy way to solve this equation. The equation is: $$ \frac{30}{15+a} + \frac{30}{15-a} = 4.5 $$ The approach I tried was multiplying both sides by $(15+a)(15-a)$ to get rid of the…
c_programmer_jim
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Proof related to factorization of a quadratic equation

Can we prove or disprove this given statement: "If a, b, and c are integers with a≠0, and the roots of the equation $$ax^2 +bx+c=0$$ are rational, then the equation can be factored as $$(ax+m)(x+n)$$ where m is an integer and n is a rational number,…
Briston
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