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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 for $a$ and $b$

How would you solve the equality: $$a\,b\,\left(b+a\right)=1$$ in terms of a and/or b? Would you subtract 1 from both sides and work from there? Or would you simply expand and work from there?
user134137
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With Trinomial's, can someone explain the purpose of the first, second and third term. In layman terms.

I know that the first term is a quadratic and I suppose that lets us know we are dealing with identifying a curve, and the third term is our constant. I just can't quite put it all together as how they are actually working together. Such as what…
Quintinium
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the quadratic equation for two unknown number

For what values of $C$ will $2x^2 + 7x + C = 0$ have? below are a few choices of the value $C$: $a)$ 2 answers $b)$ 1 answer $c)$ 0 answers
carry
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Solving quadratics using $y=a(x-p)^2+q$ ?

The vertex is $(-4, 2)$ and the y-int is $(-3,-1)$. How would I solve this, or find out what "$a$" is so I can write the equation and graph it?
user133126
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all the values of c for the equation: x^2-5x+c>2

We need to find all the values of c for this equation: x^2-5x+c>2 This question was on my exam I didn't know how to get started on the question. Could some one help me out.
user12193
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How to arrange the equation

four squares of which each side is x cm are removed from a rectangular metal sheet of dimension 20cm x 15cm at its corners to form an open box.If the volume of the box is 84 x cm3 , calculate the value of x
San San
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If $ax^2+bx+c=0$ and $2x^2 +3x+4=0$ have a common root where $a,b,c \in \Bbb N$,find least value of $a+b+c$

Problem: If $ax^2+bx+c=0$ and $2x^2 +3x+4=0$ have a common root where $a,b,c \in \Bbb N$, find least value of $a+b+c$ Solution: Here $2x^2 +3x+4=0$ will give complex roots These roots will be in pair Both equations have a common root $ax^2+bx+c=0$…
rst
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quadratic formula - getting wrong values

I know this is a stupid question but, I posted this thread up not long a go Function derivatives. I'm trying to replicate this question. However, I can't seem to work out how I got the value $-2$ and $3$ from the quadratic formula. I've tried and…
user120993
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Quadratic equation need to solve

There are these three quadratic equations: $(x - x_1)^2 + (y - y_1)^2 + P_1 \cdot h^2 = 0$ ……..(1) $(x - x_2)^2 + (y - y_2)^2 + P_2 \cdot h^2 = 0$ ……..(2) $(x - x_3)^2 + (y - y_3)^2 + P_3 \cdot h^2 = 0$ ……..(3) where we know the values of $x_1,…
user119767
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How to solve $x$ in an equation with $x^2$ and $x$ as unknowns in it?

I want to solve $t'$ in: $$ut + \dfrac{at^2}{2} = ut' + \dfrac{a't'^2}{2}$$ Where I will know the values for constants $u$, $t$, $a$ and $a'$. I believe I can reduce the above to a quadratic equation: $$2ut + at^2 = 2ut' + a't'^2$$ $$a't'^2 + 2ut' -…
markmnl
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How do I determine the maximum value for a quadratic equation on an interval?

I need to determine the maximum value for y = ax^2 + bx + c, where I know the coefficients and the upper and lower x values. Say the input values are: a = 5 b = 1 c = 2 x lower limit = -5 x upper limit = 5 Given these input, how do I determine the…
Zolt
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Finding a+b+c+d where a,b and c,d are the roots of two different quadratic equations

If $a, b$ are the roots of the equation $x^2-10cx-11d=0$ and $c,d$ are the roots of the equation $x^2-10ax-11b=0$ (where $a\ne b\ne c\ne d\ne 0$), then find the value of $a+b+c+d$. I have the following…
Tejas
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Find the integer n

Let $a$ and $b$ be two integers such that $10a+b=5$ and $p(x)=x^2+ax+b$. Find the integer $n$ such that $p(10)p(11)=p(n).$ Please tell how to proceed.
Tejas
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Find a if the equation has a solution

If this equation has a solution, then 'a' is equal to None of these How should I proceed in this problem?
Tejas
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1 answer

Algebra steps breakdown

I have been reviewing this question. : How can I find the points at which two circles intersect? Although during the answering steps I got a little stuck: From this: 17y2−62y+49=0 To this: y=(31+82√)17 I am not 100% on the steps taken to achieve…
RacconLauncher
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