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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Solve quadratic equation by completing square

We have a equation: $2x^2+7x+3$ I tried to find the vertex of the parabola by this formula: $a(x-h)^2+k$ but I could not get it. I got this: but it is not right. $2(x^2+ \frac{7}{2}x+\frac{49}{4})+3-\frac{49}{2}$ What's the problem? Is it possible…
Ehsan Zehtabchi
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Max no of real roots

$p(x) =x^6 + ax^5+ bx^4 +x^3 + bx^2 + ax + 1$ Given that p(1)=0 but p(-1) is not zero. What is maximum number of distinct real roots of p(x)? I divided by $x^3$ and made a cubic in t, where $t=x+1/x$, but after that what can i say? My cubic is $t…
maveric
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Interval Notation of the Increasing and Decreasing Sections of a Quadratic

This is the quadratic y=-4x^2+4x+3. Here is the graph. I know that the increase and the decrease of a graph has to do with the y value. From this, I know that from negative infinity to 0.5, the function is increasing. From 0.5 to positive infinity…
mjj
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Are my solutions to these quadratic questions correct? (6 questions)

The side length of a square is 4m. When each side is increased by the same amount, the area of the square doubles. By how much did the side length increase? $4^2 = 16$ = original area $(4+x)^2 = 16^2$ $(4+x) = \pm 16$ $x = 12, -20$ but $-20$…
user477465
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How many of the following expressions (quadratics) factor for $n \leq 2018$

I know that $x^2+x-1$ does not factor over the integers but $x^2+x-2$ does (i.e.: (x+2)(x-1)). If I have expressions of the form $x^2+x - n$ $\forall n \leq 2018$, how many of the expressions factor for $n \leq 2018$? I'm trying to notice a pattern…
user8358234
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Finding values in triple bracket question (algebra)

How would I find the valued of $p$ and $q$ in the equation: $$(x+p)(x+q)(x+5)= x^3+8x^²-3x-90$$ Any answers are well appreciated!
Adrian
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Quadratic function approximation

I just have a quick question on quadratic equations, if we are given a whole bunch of data when plotted, it gives us some quadratic relationship. But I tried to use the old fashioned way to find this approximate equation by finding $c$ at $x =0,$…
Aurora Borealis
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Irrational roots of an equation

If $f(x)=ax^2+bx+c$ has an irrational root, if $u=\frac{p}{q}$ be any rational number. a,b,c,p and q are integers. Prove that $\frac{1}{q^2}\le|f(u)|$ My approach $b^2-4ac>0$,$b^2-4ac\ne k^2$, $k$ is a rational…
Samar Imam Zaidi
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Least integral value alpha of x such that

Question: My solution: According to me -6 is least possible integer which satisfies option d. Textbook's solution I don't understand what I'm doing wrong. Thank you for your help.
user3508140
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How to solve for x using the quadratic equation when there are multiple variables?

Can someone please help me solve for $x$ using the quadratic formula for this question? I am not sure how to set this up. $x^2+2ax-4b^2$
Eliza Nguyen
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quadratic formula question deriving from completing the square

If you derive the quadratic formula by completing the square on a general quadratic, then should the denominator end up as $2 \ \text{modulus(a)}$ where $a$ is the coefficient on the $x^2$ term which may well be negative? I know it doesn't matter in…
Carlos Bacca
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Equilibrium from linear to quadratic

I have this: $Qd = 21 − 6P$ $Qs =−6+30(P − 0.9)$ I'm asked to solve P and Q at equilibrium. If I'm not mistaken, $P=1,5$ (because $21 - 6P = -6 + 30P - 27$) And Q is: $21 - 6*1.5 = 12$ I hope it's right. Now the tricky part is to determine the…
Bachir Messaouri
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to get the quadratic equation for a given formula

I have a formula $A=-\frac{u'(a)}{u(a)}$ such that $u(a)=u(0)s(a)+u'(0)q(a)$ and $u'(a)=u(0)s'(a)+u'(0)q'(a)$ , I was asked to find the quadratic equation for $A$ .. I know it means I have to find the coeffiecents $a$,$b$,and $c$ in the formula…
S.N.A
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How to avoid introducing a spurious solution?

Suppose I have $\sqrt{r-x}-\frac{x}{\sqrt{r-x}}-o=0$ with $r,x$ and $o$ real. To solve I multiply by $\sqrt{r-x}$. I assume therefore $r>x$ $r-x-x-o\sqrt{r-x}=0$ $r-2x=o\sqrt{r-x}$ Squaring $(r-2x)^2=o^2(r-x)$ This is a second order equation,whose…
Fabio Dalla Libera
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Quadratic equation sum from Russian book

Solve $\sqrt{5-x}=5-x^2$ for $x$. This is what I have done so far. Method 1: \begin{align} \sqrt{5 - x} & = 5 - x^2 \\ 5 - x & = (5 - x^2)^2 \\ 5 - x & = 25 - 10x^2 + x^4 \\ 0 & = x^4 - 10x^2 + x + 20 \end{align} Method 2: \begin{align} \sqrt{5 -…
L Lawlit
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