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
1
vote
1 answer

How to find sum of quadratic

I got this quadratic function from physics that I need to find the sum of each term, up to whatever point. Written thusly: $$ \sum_{n=1}^{t}4.945n^2$$ And is there someway to quickly figure this out? Or links to tutorials
Gᴇᴏᴍᴇᴛᴇʀ
  • 915
  • 2
  • 14
  • 28
1
vote
0 answers

Common roots of quadratic equations

If $x^2-ax+b=0$ and $x^2-cx+d=0$ have a common root, then show that $ab,bc,ad $ are in an arithmetic progression When I use the relationship for the common root for qudratic equations, i end up with $(c-a)(ad-bc)=(b-d)^2$. By solving this i cannot…
user345749
  • 23
1
vote
2 answers

Quadratic equations (roots real)

Complete set of real values of $a$ for which the equation $x^4-2ax^2+x+a^2-a=0$ has all its roots real? My attempt: I tried to make a quadratic in $x$ so that i could use $D>0$ condition but it doesn't lead me to values of $a$
user383555
  • 327
1
vote
2 answers

Dividing by negative number in quadratics, yielding totally different result.

forewords: Honestly, I've tried looking around for any answer to this question, but it's so specific i can't find any. If it's already answered i apologise. Alright so i have this equation $$-x^{2}+4=0$$ Now usually i would remove the negative in…
Aron
  • 409
1
vote
1 answer

What technique reduces factorable ax^2+bx+c=0 to factorable where a=1

The normal way to factor ax^2+bx+c=0 is to look for t,u,v,w such that: (tx+u)(vx+w) = 0 so that tv=a, uw=c, and uv+wt=b. This can be tricky, since there can be several possibilities for t,u,v,w. Ashley, a bright student, showed me a shortcut…
user2469
1
vote
1 answer

Show that the equation cannot have imaginary roots

Show that the equation $$ \dfrac{a}{x-1} + \dfrac{b}{x-2} + \dfrac{c}{x-3} + \dfrac{d}{x-4} = 1 $$ cannot have imaginary roots if $a, b, c, d$ are any four real numbers of the same sign. I tried putting $x = a$ and some other variables to show that…
bulbasaur
  • 901
1
vote
2 answers

How do I go from $33/64 - 2x + x^2 \longrightarrow \bigg(x - \frac{2 + \sqrt{4 +33/16}}{2}\bigg)\bigg(x - \frac{2 - \sqrt{4 +33/16}}{2}\bigg)$?

How do I go from $\frac{33}{64} - 2x + x^2 \longrightarrow\bigg(x - \frac{2 + \sqrt{4 +33/16}}{2}\bigg)\bigg(x - \frac{2 - \sqrt{4 +33/16}}{2}\bigg)$ and then to $\big(x - 1-\frac{\sqrt{33}}{8}\big)\big(x - 1 + \frac{\sqrt{31}}{8}\big)?$ For the…
Daniel Cortild
  • 485
1
vote
2 answers

Acceleration using time and distances

A car crosses 10m distance from point A to point B in 1 second, next 10m distance from point B to point C it crosses in 0.8s. Having distances and times is it possible to calculate acceleration and speed at points A,B,C?
Zijo
  • 13
1
vote
3 answers

Factoring Polynomial using Quadratic Equation

I'm trying to use the quadratic equation (QE) to factor a degree 2 polynomial into the format: $(x + a)^2$, where a is any real number. This works great for equations like: (1) $x^2 + 2x + 1$ The QE gives roots $x = \{-1, -1\}$, and $(x + 1)^2 = x^2…
Henry Rillovian
  • 25
1
vote
3 answers

If the roots of the equation are integers then find the value of $k$.

The question says roots of $x^2-kx+36=0$ are integers then the number of values for $k$ are? I know roots are integral if discriminant is a perfect square of an integer, but using this I get infinite values for $k$. Which values should I reject?
danny
  • 357
1
vote
5 answers

On the number of possible solutions for a quadratic equation.

Solving a quadratic equation will yield two roots: $$\frac{-\sqrt{b^2-4 a c}-b} {2 a}$$ and: $$\frac{\sqrt{b^2-4a c}-b}{2 a}$$ And I've been taught to answer it like: $$\frac{\pm\sqrt{b^2-4a c}- b}{2 a}$$ Why does it yields only two solutions?…
Red Banana
  • 23,956
  • 20
  • 91
  • 192
1
vote
4 answers

where is my mistake with this equation ot hyperbolic problem?

Let parabola $\Gamma_{1}:$$y^2=4x$,and hyperbolic curve $\Gamma_{2}$: $x^2-y^2=1$.it is well known this two is symmetric.so the two point $A$ and $B$ about $x$ axial symmetry,or mean $x_{A}=x_{B}$.see figure, but we…
math110
  • 93,304
1
vote
1 answer

Solving for x in equations with large negative exponents

I am working on a problem that asks me to solve for x for an iteration of the Lennard-Jones equation. Specifically, I am trying to determine the equilibrium separation between two hypothetical atoms. The equation is given to me as: PE(x) =…
1John5vs7
  • 113
1
vote
6 answers

How to solve without solving by inspection? $\frac{x+5}{x+k}=\frac{-kx+5}{x-1}$

Background: This is from a test review on functions. The original problem was Find the value of $k$ so that the function $f(x) = \frac{x+5}{x+k}$ will be its own inverse. I found the answer by inspection, and then tried to solve it through more…
Jack Pan
  • 1,704
1
vote
2 answers

Quadratic inequality proof.

I recently encountered a quadratic equations property that $ax^2+bx+c>0$ $ \forall$ $x\in \Re \Rightarrow D<0$ $and$ $a>0$ and $ax^2+bx+c<0$ $ \forall$ $x\in \Re \Rightarrow D<0$ $and$ $a<0$. Now, i tried to prove it algebraically and…
Harsh Sharma
  • 2,369
1 2 3
…
64 65