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
2
votes
1 answer

Clarification on forming a quadratic equation given the roots

I am confused about the roots and how they can be used to construct the original quadratic equation. If I am given the roots of the quadratic equations as $2$ and $3$ I can generate the original equation as $(x-2)(x-3)=0$. Is this right? Now Let's…
Rahul
  • 21
2
votes
1 answer

quadratic formula returning one real solution when none should exist

i rely a lot on the quadratic formula, but i'm learning to grow a little wary of it. or of how i use it. for example if the "A" term is zero (ie your curve is a line) then the quadratic divides by zero. in the course of calculating the tangents of a…
orion elenzil
  • 125
  • 3
2
votes
1 answer

Transforming a quadratic from its zeroes

In below problem I've been trying to figure out how simply letting $y=\dfrac{x}{x+10}$ gives the quadratic with roots scaled by $\dfrac{1}{\alpha+10}$. I'm a bit clueless why it works. My thoughts : - To get a quadratic $g(x)$ whose roots are $k$…
AgentS
  • 12,195
2
votes
4 answers

$ ax^2 + bx +6 $ does not have two distinct real roots , then what will be the least value of $ 3a + b $?

$ax^2 + bx +6$ does not have two distinct real roots , then what will be the least value of $3a + b$? I know that $D$ will be less than or equal to. But least value of $3a + b$ can not be deduced from that. Can anyone please help me?
cmi
  • 3,371
2
votes
1 answer

Quadratic Equations in two-variables.

Determine the number of ordered pairs $(x, y)$ of positive integers satisfying the equation $x^2+y^2-16y=2004$. My solution: $x^2+y^2-16y=2004$ $\Rightarrow x^2=2004-y^2+16y$ $\Rightarrow x=\sqrt{2004-y^2+16y}$ Now, plugging in integers on the…
Math Tise
  • 657
  • 1
  • 5
  • 11
2
votes
6 answers

Square root in quadratic equation

I ran into a Math problem in which I was told to solve like that: \begin{align} x^ 2 - 25 &= 0 \\ x^2 & = 25 \\ x & = \sqrt{25}\\ x & = 5 \end{align} I wonder what the logical and also intuictive explanation might be on removing the power of x and…
Matheus Minguini
  • 159
2
votes
2 answers

Solving an cubic equation

This comes from a chemistry question but it is the maths I am struggling with. I solved the determinant of a $3 \times 3$ matrix to get: $$(a-E)^3 - 3B^2(a-E) + 2B^3 = 0$$ I need to solve this in terms of $a$ and $B$. So for example $E = a + 2B$. If…
Henry Cooper
  • 25
2
votes
2 answers

Simple question regarding factoring quadratics

Say we have an equation $ax^2 + bx - c = 0$ and want to find $x$. Obviously the way to solve would be to use the quadratic equation or factorize. I understand that saying $$ax^2 + bx = c => x(ax + b) = c$$ and then solving is wrong (the values of…
CAF
  • 2,850
2
votes
2 answers

Finding integer solutions to a quadratic equation in 2 variables

We have an equation $x^2+4y^2-2xy-2x-4y-8=0$. Find all integer pairs $(x,y)$ satisfying this equation. I did some research on my own, and found that the above equation describes an ellipse. But I'm not sure how it helps. Is there any systematic way…
user406287
  • 349
  • 2
  • 10
2
votes
4 answers

Equation solving involving terms inside roots

How do I solve $$\left(x-\frac{1}{x}\right)^{1/2}+\left(1-\frac{1}{x}\right)^{1/2} = x$$ My Try I tried to take the first term as $t$ but then I had to square both sides twice and that led to a complex bi quadratic. I'm not sure even that'll solve…
Tanuj
  • 830
  • 6
  • 24
2
votes
1 answer

Expressing the roots of a quadratic equation in terms of the roots of another quadratic equation

Question: Express the roots of the equation $q^2x^2-(p^2-2q)x+1=0$ in terms of those of $x^2+px+q=0$ My attempt: Roots of the second equation are $\frac{-p±\sqrt{p^2-4q}}{2}$ Roots of the first equation are…
MrAP
  • 3,003
2
votes
3 answers

The greatest revenue?

A theatre seats 2000 people and charges $10 for a ticket. At this price all the tickets can be sold. A survey indicates that if the ticket price is increased, the number sold will decrease by 100 for every dollar of increase. What ticket price would…
Violet Huras
  • 21
2
votes
1 answer

Wavy curve method (equations)

Can someone state the wavy curve method and explain its various rules along with proofs? And is it applicable for quadratic equations only or any equation of $n$th power (if we can find it's roots?)? Can we use wavy curve method for equations whose…
Mathejunior
  • 3,344
2
votes
6 answers

If $n^2+4n+10$ is a perfect square, then find the possible integer values of $n$.

If $n^2+4n+10$ is a perfect square, then find the possible integer values of $n$. I couldn't understand what the question is asking me to do. I could only do one step that would equate it to $k^2$ after that I wasn't able to solve it.
Hary
  • 21
2
votes
4 answers

Show $x^2 +xy-y^2 = 0$ is only true when $x$ & $y$ are zero.

Show that it is impossible to find non-zero integers $x$ and $y$ satisfying $x^2 +xy-y^2 = 0$.
mathberry
  • 31
  • 3
1 2 3
…
64 65