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 $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

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The solution set of a multivariate quadratic after transformation of variables

I have an equation given in terms of three vectors $\vec{x}$, $\vec{y}$ and $\vec{z}$, all in $\mathbb{R}^n$: $$1 - (\vec{x}\cdot\vec{y})^2 = K + 2K\vec{z}\cdot\vec{y} + (\vec{z}\cdot\vec{y})^2, K \in \mathbb{R}$$ I want to solve for both $\vec{x}$…
Michael Stachowsky
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Graphs and Quadratic Equations?

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 ball hit the ground? What I've tried so far: I have…
Hanka
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Simple Quadratic Question Word Problem

On a site, I read a word problem: A company charges 1.25 per ride and currently averages 10000 riders per day. The company needs to increase revenue, but found that each $.10 increase in fare results in a loss of 500 riders. What should company…
user342258
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Am I finding this $x$-value correctly?

If the flight path of a cricket ball is given by: $$y = \frac{1}{3}x - \frac{1}{60}x^2$$ And a fielder standing originally at $(10, 0)$ catches the ball when it is $1.5$ units above the ground, to find how far he ran you would simply sub $1.5$ in as…
Tiernan Watson
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Solving octic equation using quadratic formula

According to the wikipedia article on octic equations, octic equations of the form $ax^8 \pm bx^4 \pm c = 0$ can be solved using the quadratic formula. How might one actually do this?
MrKagouris
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Value of qudaratic equation

In my exams, I was asked to calculate value of Quadratic Equation from given value of a, b, c & x. I'm not good in mathematics. Does that refers to calculating roots of quadratic equation? As far as my knowledge is x is root of Quadratic equation…
Adnan Umer
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Roots of a quadratic equation

If $ a $ , $b$ are the roots of $ x^2+x+1=0 $ , then the equation whose roots are $a^k $ and $b ^k$ where k is a positive integer not divisible by 3 is $a)$ $x^2 - x + 1 = 0$ $b)$ $x^2 + x+1 = 0$ $c)$ $ x^2 -x -1 =0$ $d)$ None of the above My…
Noob101
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Simplifying a solution to a quadratic equation

I am solving: $(\sigma_A^2 - 2\rho\sigma_A\sigma_B +\sigma_B^2)x^2 +2(\rho\sigma_A\sigma_B - \sigma_B^2)x +\sigma_B^2 = 0$ I need to show that a real $x$ exists if and only if $\rho = \pm 1$ Using the quadratic formula I could only get as far as $…
damson_jam
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Existence of rational roots in a quadratic equation

Consider the quadratic equation $(a+c-b)x^2 + 2cx + b+c-a = 0 $ , where a,b,c are distinct real numbers and a+c-b is not equal to 0. Suppose that both the roots of the equation are rational . Then a) a,b, and c are rational b)$c/(a-b)$ is rational…
Noob101
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Formulate quadratic equation

Here is an equation $$r^3-5r^2+8r-4=0$$ Is there a way I can formulate a quadratic equation from this? Sorry if the question seem dumb, I am stuck and I can't figure a way out.
Diamond
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I don't understand how the following algebraic equation breaks down. I just can't figure out how this answer is devised.

I just don't understand how this equation breaks down like this. The second step... $[k^2 + k + 2k + 1]$ is perplexing, but breaking that down to $(k+1)(k+2)$ has completely baffled me. I would expect this to be equivalent to $[k^2 + 2k + 1k +…
Nicholas
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The nature of roots of the quadratic equation $ax^2+(b-c)x-2b-c-a=0,$

If the expression $ax^2+2bx+c$, where $a$ is a non-zero real number, has the same sign as that of $a$ for every real value of $x$, then roots of the quadratic equation $ax^2+(b-c)x-2b-c-a=0$ are: (A) real and equal (B) real and unequal (C) non-real…
Brahmagupta
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Why are these 2 algebraic expressions equivalent?

I just solved a long problem for my physics w/calculus homework that required a simplification using a quadratic formula. The "textbook" (flipItPhysics) came up with a different simplification than mine but it turns out they are equivalent. I can't,…
Josue Valverde
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how to solve the following quadratic word problem *updated*?

The total cost of carpeting a rectangular room is given the expression $$6x^2 + 18x$$ Which situation best describes the expression? The length of the room is 6+2x feet, its width is 2x feet, and the cost of carpeting is $1.50per square foot. The…
MATH ASKER
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If $2$ is subtracted from each root,the results are reciprocals of the original roots.Find the value of $b^2+c^2+bc.$

The equation $x^2+bx+c=0$ has distinct roots .If $2$ is subtracted from each root,the results are reciprocals of the original roots.Find the value of $b^2+c^2+bc.$ Let $\alpha$ and $\beta$ are the roots of the equation $x^2+bx+c=0$. According to…
Vinod Kumar Punia
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