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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Solving $4-q-q^2 = 1+4q+q^2$

Given a market demand function: $$p=4-q-q^2$$ and the market supply function: $$p=1+4q+q^2$$ We can solve for: $$4-q-q^2 = 1+4q+q^2$$ When I move the terms from right to left, I get $3-5q-2q^2$, but from left to right $2q^2+5q-3$. I understand…
Dan
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Finding the Missing Zero of the Quadratic

Given that $ f(x)= ax^2+bx+c$, where $b = a + 1$ and $c=b+1$. One zero of the function is $x=6$. Find the other zero of $f$. I actually have the answer to the question but only a brief explanation of some of the steps. If I define $R$ to be the…
user3753
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How to know if a quadratic equation can be equal to zero?

How to check by a fixed algorithm/formula for the possibility of these: x^2 + x + 1 = 0 AND 2x^2 + 4x - 2 = 0 AND x^3 + 3 = 0
Sachin Chaudhary
  • 49
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solving equations involving 3rd degree

I got the below question x^3-10x^2+Px-30=0 find the value for P. How this can be answered? If I give different values for x, it gives different values for P. Is this question wrong?
Hari
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Finding the y-intercept

The graph of the quadratic function y=(x-h)²+k passes through (3,7) and (4,11). The axis of symmetry is the graph is x=2. How can I find the y -intercept of the graph？ I know that it is the value of k (the minimum value of the function) but how…
Estudiantekriss
  • 313
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4 answers

Finding x in quadratic function

The sum of two numbers is 10. If the sum of their squares is a minimum, what are the two numbers? I can't think of how to write an equation to solve this question as I dont know what are the coordinates of the vertex. Can anyone please teach me?…
Estudiantekriss
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Solving quadratic equation

From $X^2 - 2X(1-X) - (1-X)^2 = 7$ I get $X^2 - 2X + 2X^2 - 1 - 2X + X^2 - 7 = 0$ Which then becomes $4X^2 - 4X - 8 = 0$. However, this should become $X^2 = 4$ how is this ?
Dan
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Question about quadratic equation

Suppose a quadratic equation whose roots are 3 and -2, so the equation is (x-3)(x+2) = 0 So, from here we get, x-3 = 0 and, x+2 = 0 Since, both equations equal to zero, we can equate these two, x-3 = x+2 So, -3 = 2 ? Where did I go wrong?
Sachin Chaudhary
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When roots are equal

If the roots of the equation $(b-c)x^2$$+ (c-a)x +(a-b)=0$ are equal then we have to prove $2b=a+c$ . I tried it by doing D=0 , but not able to solve it . Please help
Koolman
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Quadratic equation positive roots.

I have a question which says that if the roots of the equation $$x^4-12x^3+cx^2+dx+81=0$$ are positive, then what is the value of $c$ and $d$. I am currently doing High school algebra and haven't had any calculus training and I believe that this…
Harsh Sharma
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Quadratic Equations conceptual doubt.

Whenever there is an equation of odd degree, it certainly carries at least one real root and this is clear to me through the graphs of any odd degree polynomial since it has to change its value in the negative side hence it must go through cutting…
Harsh Sharma
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Need help with solving quadratic equations on Khan Academy

In the screenshot below, you'll see the correct answer is x = -9 or x = -7. I wrote x = -7 or x = -9 and got it wrong. I do not understand why one is right and the other is wrong as it doesn't matter which order you write them in the factored…
OwenAlexander
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Intersections {x^2/y+y^2/x=25 and 5-x^2=y}

I did run in to this problem last week in school and it was supposed to be solved with algebra. This isn't just two quadratic equations Solve all intersections x^2/y+y^2/x=25 5-x^2=y Spoiler I did get this two …
Alfons Marklén
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how do you solve $1.08=(1+x)^{1200}$?

How do you solve $$1.08=(1+x)^{1200}?$$ Thanks so much for any guidance.
nishman
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Solve $2x(1+\frac{1}{x^3})+7(1+\frac{1}{x})=0$ without cubic formulas and such

Just like in the title, I wonder if there is a way to solve $2x(1+\frac{1}{x^3})+7(1+\frac{1}{x})=0$ without any use of solving cubics including the rational root theorem (with these methods I already got $x=-2,-1,-\frac{1}{2}$). The original…
Theorem
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