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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About roots of quadratic trinominals

How can I prove that we can find a point $(p;q)$ on the graph of the trinominal $x^2+bx+c=0$ that has only one root, that makes the equation $x^2+px+q=0$ have one root?
student28
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Simple Questions about Quadratic equations with 2 variables.

I would like to know, step by step, how to solve the following equation. I already know the roots, but I would like an explanation. Thanks in advance. $$x^2+19x+48=m^2$$ I use $$m^2$$ to indicate perfect squares so the question is: how can i find…
Alessandro Fenu
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If one of quadratic equations doesn't have roots, the other one has them

There are two equations: $x^2+2p_1x + q_1 = 0$ and $x^2 + 2p_2x+q_2 = 0$. It is also known that $q_1+q_2 = 2p_1p_2$. How can I prove that if one of them doesn't have roots, then the other one has the roots? So I have $$4p_1^2 - 4q_1 < 0$$ I need to…
idliketodothis
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Other factors of the equation $2x^4 + 4x^3\sin A\sin B -\cdots$

If $x^2+x\cos(A + B) + 1$ is a factor of the expression, $$2x^4 + 4x^3\sin A\sin B -x^2(\cos 2A +\cos 2B) + 4x\cos A\cos B -2$$ Then we have to find the other factor (s). I am not getting start Can anybody provide me a hint .
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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what does power of $2$ in $x^2$ represent

If $y = Bx + c$, and B for x is the slope, how about in $ y = B_{1} x^2 + B_{2} x + c$, what do you call the $B_{1}$? I am trying to defined it in a paper and need to know what is the term called. I am defining something like where c is the…
Sharah
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Quadratic Equation Quesiton

IF $a>0$ and $b<0$, which of the following statements are true about the value of (x) that solve the eq0ution $x^2 - ax + b = 0$ a)they have opposite signs b)their sum is greater than zero c)their product equals $- b$ Now my choice was a) and c),…
mike
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Is answer incorrect for this quadratic equation?

I am solving the following question on quadratic equation and I always get $p = -6$ as answer but the answer in book is $p = 3$. Question What am I missing in my solution or is the answer mentioned in book incorrect? Problem For the equation…
Sunil
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Simplify equation with square and non-square $y$

I'm trying to solve a few equations but my math is a bit (very) rusty. In particular, I've simplified one of them to this: $$2y^2-3y-2=0$$ I can see that the answer is "2" but how can I prove it? Is it possible to simplify the equation further?
laurent
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Quadratic fit data sufficiency

I would like to fit a quadratic curve to some data: Label X Y S 0 105 E 277 85 Min m 72 Min is the minimum of the curve. My aim is to find m. (I suspect m is around 400 to 500) a) Is this possible given this amount of data? b) If…
Lobert
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How to prove $\forall a,b,x \in \mathbb N \exists c,d \in \mathbb N\setminus${$a,b$}$: (x-a)(x-b) = (x-c) (x-d)$

The statement $\forall a,b,x \in \mathbb N \exists c,d \in \mathbb N\setminus${$a, b$}$: (x-a)(x-b) = (x-c) (x-d)$ seems to be true for me. But I really have no idea how to prove it formally. Is there a way?
M. Dou
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Is this expression a perfect square?

Show that the expression $$(x^2-yz)^3+(y^2-zx)^3+(z^2-xy)^3-3(x^2-yz)(y^2-zx)(z^2-xy)$$ is a perfect square and Find its square root.
Lelouch vi Britannia
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What is the solution to the following quadratic equation in $\mathbb R$?

$ x^2+\sqrt{d}x+d = 0 $ , Where $d$ is the real number whose integer part is $0$ and it's $n$-th decimal digit is given by (for $n>0$): $ \text{NthDecimalDigit}(n) = \left \{ \begin{array}{l}0,\: \:\: \text{if $2n+2$ can be expressed as the sum of…
George Bougioukas
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Quadratic equation in a graph

The question is why does the line with equation ax+by+c=0 has a negative slop is wrong? I get a and b<0 by -b/2a , is it correct to proof the values in this way? However, when I try to calculate its slope by -a/b, it is a negative slope. I have no…
Estudiantekriss
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An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind.

An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind.The total flying time is 3 hrs 20 mins and the airplanes speed in still air is 600 km/h what is the speed of the wind?
Sam
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how do I get the tangent coordinates if I am given the quadratic function and the slope(gradient)

I have the following task: calculate the coordinates of the intersections point between a straight line with a given slope and a quadratic function, so that you only receive one intersection instead of the normal two or none. I am given the slope…
user2741831
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