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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We have the equation $2x^2-\sqrt{3}x-1=0$ and have to find $|x_1-x_2|$

We have the following quadratic equation: $2x^2-\sqrt{3}x-1=0$ with roots $x_1$ and $x_2$. I have to find $x_1^2+x_2^2$ and $|x_1-x_2|$. First we have: $x_1+x_2=\dfrac{\sqrt{3}}{2}$ and $x_1x_2=-\dfrac{1}{2}$ So…
keylin.rion
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If 2C8$\cdot$3C1$=$90C58, what is C?

I recently came across this question: If C is a digit such that the product of the three-digit numbers $2C8$ and $3C1$ is the five-digit number $90C58$, what is the value of $C$? I start by multiplying out the two three digit numbers and…
Max0815
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Solving a quadratic formula with positive discriminant yields only one correct solution.

I'm a math tutor at a small university. One of my students asked me about the problem, $$p - 2\sqrt{p} = 15$$ Solving this, we found, in sequence, $$-2\sqrt{p}=15 - p$$ $$4p = p^2 - 30 p + 225$$ $$p^2 - 34 p + 225 = 0$$ then, using quadratic…
Natalie Webb
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Find the number of values of $a$?

Consider a quadratic equation; $$ x^2 + 7x – 14(a^2 + 1) = 0,$$ … (where $a$ is an integer) For how many different value of $a$, the equation will have at least one integer root? I found out its discriminant, it comes out to be $$ (49 +…
vikiiii
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Find the roots of quadratic polynomial given one root of another quadratic polynomial?

if $a,b,c$ are Real numbers and $1$ is a root of equation $ax^2+bx+c=0$ then curve $y = 4ax^2+3bx+2c$ , (a is not zero) intersects $x$ axis at how many points? I get a relation $a+b+c = 0$ I tried substituting this in given polynomial and tried…
Matt
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Is -2 is a root of the equation : $\sqrt {x^2 - 8} = \sqrt {3x + 2}$?

Is -2 is a root of the equation : $\sqrt{x^2 - 8} = \sqrt{3x + 2}$ ? Is it any limitation of the root of this equation? If the root is -2, both sides of the equation are equal to 2i. Is this acceptable since the variable x has no limitation.
joe
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Can anyone help me solve this?

Two taps A and B can fill a swimming pool in $3$ hours. If turned on alone, it takes tap A $5$ hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool? \begin{align*} 3(A+B) & = x\\ \frac{x}{B} - \frac{x}{A} &…
Chin Huan
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Intuitive understanding of factoring quadratic equations

When factoring a second degree equation $ax^2 + bx + c$ you find the roots then take $a(x - \text{root})(x - \text{root})$. I am wondering why this works. Sorry if poorly phrased question.
plebian
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If an equation has multiple roots of same value , What does it signify?

$(x-1)^{560}$ is said to have 560 roots. Now , all the roots must be 1(since it is the only factor tha can be formed ). And another example is $x^2 - 2x + 1 = 0 $ , Here $ x = 1$ ,only root as answer. Q1 By saying $560$ roots , It does not give an…
Rider
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Factoring quadratics with certain property

I am looking into which quadratics factor with the following property: $x^2±ax±b$ factors e.g. all the following factor for $a=5, b=6$ $x^2+5x+6=(x+2)(x+3)$ $x^2-5x+6=(x-2)(x-3)$ $x^2+5x-6=(x+6)(x-1)$ $x^2-5x-6=(x-6)(x+1)$ I have found $x^2+10x+24,…
Bob
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Quadratic equation where constant term is an integral function

Consider a quadratic equation ${x^2} + 2x = k + \int\limits_0^1 {\left| {t + k} \right|dt}$. Then choose the correct option(s), (A) Roots are Real (B) Roots are Imaginary (C) Roots are Distinct (D) Roots are complex number My approach is as…
Samar Imam Zaidi
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Apporoaches to solve the given algebraic expression

If $\displaystyle \ \ x^{4} \ +\ x^{2} \ =\ \frac{11}{5}$ then what is the value of the given expression $$\displaystyle \left(\frac{x+1}{x-1}\right)^{\frac{1}{3}} +\ \left(\frac{x-1}{x+1}\right)^{\frac{1}{3}} \ =\ \ ?$$ My Try : As I can find…
Girish Kumar Chandora
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Easier way to find amount of solutions between a line and quadratic?

Is there a better way of finding the number of solutions of the system: $y=(x-7)(3x+4)$ and $x=3y-1$ that doesn't involve calculus? I know these are $2$ but that's due to substitution of one equation into the other and finding the discriminant of…
user612996
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Given 3 points, how can I find a quadratic equation that intersects all of these points?

Given 3 points, $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, how might I find an equation intersecting all of these points? Given just 2 points, to find a linear equation, this is the formula: $$y\…
MazeOfEncryption
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The zeroes of the function $f(x)=x^2-ax+2a$ are integers. Find all possible values of a.

So far I have only got 9 from just guess and check. I am thinking of using Vieta's Formula, but I am struggling over the algebra. Can someone give me the first few steps?
Gerard L.
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