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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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The equation $x^2+px-p$ has two real and different solutions $x_1$ and $x_2$ for which $1<(x_1/x_2+x_2/x_1)<3$ for which interval of $p$?

This is a multiple choice question, but I figure it will be easy enough to do without the given answers. It seems like an easy question. Use Vieta's formula from the inequality and define $p$ from that. But I'm making some stupid mistake somewhere…
John Doe
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Difficulty turning a quadratic equation to "vertex"-form

I'm having difficulty reducing a quadratic equation to its "vertex-form" by following my textbook and nearly every tutorial I can find online. The starting equation is: $$f(x) = -2x^2 + 16x - 24$$ Next, I divided each term by $-2$ (to leave the…
Carcigenicate
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Relationship between roots and equations

I'm stuck on topic of relationship between roots and equations. The roots of $x^2 -2x +3 =0$, are $\alpha$ and $\beta$. Find the equation whose roots are : 1- $\alpha+2$, $\beta+2$ 2- $\alpha^2$, $\beta^2$ I know what the basis are like…
A-levels student
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Show that quadratic is positive for all real values of x

I have been asked this question: Show that $x^2 + 2px + 2p^2$ is positive for all real values of $x$. I've worked it out like so: Discriminant = $(2p)^2 - (4\times 1\times(2p^2)) = 4p^2 - 8p^2$ I realise that the discriminant must be $\le0 $ No…
Charon
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fitting a quadratic to 3 coordinates

say I have 3 points on the plane (Cartesian coordinate system), (a,b), (c,d) and (e,f), I am fairly certain that there is one unique quadratic curve which passes through each point. what is the formula $(y=ux^2+vx+w)$ for the curve in terms of a, b,…
stanley dodds
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Quadratic Equation Roots Prove

I have a question in my textbook from chapter of quadratic equations from exercise of sum of roots and product of roots that; Prove that the equation $$ a x^2 + b x + c = 0, \quad a > 0 $$ has both roots positive, iff $b < 0$ and $c > 0$. both…
Muhammad Salman
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solve for x in the following Quadratic equations

I am not able to solve this problem for my son. Is ther any error in the question itself. $\dfrac{1}{(x+1)} + \dfrac{1}{(x+5)}=\dfrac{1}{(x+2)}+\dfrac{1}{(x+4)}$. Thanks in advance..
user215883
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Help finding the exact form through quadratic formula

Question: $$\frac{5m}{2}=2+\frac{1}{m}$$ I have attempted the question but my answer is not correct according to the book. $$\frac{5m^2}{2m}-2=0$$ $$5m^2-2=2m$$ $$5m^2-2m-2=0$$ When I placed my following working out into the quadratic formula my…
006609
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All solutions to Quadratic matrix polynomials

I am after two things: 1- algorithms for finding all solutions of possibly large quadratic matrix equations of the form $AX^2+BX+C=0$ 2- (if possible) software implementing the algorithms Everything except Grobner basis based methods. Thanks, Pat
Pat Mboma
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If $ax^2+bx+6=0$ doesn't have $2$ distinct real roots, then find the least value of $ (3a+b)$

If $ax^2+bx+6=0$ doesn't have $2$ distinct real roots, then find the least value of $(3a+b)$ $a,b\in \mathbb R$ Any hint for this question?
Harshal Gajjar
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Polynomial function question

If $f(x)$ is equal to $\frac{1}{x^3 + 3x^2 + x}$, find the smallest value of $n$ for which $f(1) + f(2) + ... F(n) = \frac{503}{2014}$. I tried noting that first initial values of f sum to $\frac{1}{5}$, and $503$ divided by $2014$ is approx…
user164403
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Determine all values of n such that this quadratic

Determine all values of $n^2 + 19n + 99$ is a perfect square. I tried setting some square $b^2$ equal to the following, and then factoring as a Diophantine equation with $2$ variables... Didn't work.
user164403
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solve quadratic equation

I'm trying to solve the following equation $2t^2 + t - 3 = 0$ I start by dividing by 2, $t^2 + \frac {t}{2} - \frac {3}{2} = 0$ Then I solve for t $t = - \frac{ \frac {1}{2} }{2} \binom{+}{-} \sqrt{(\frac {1}{2})^2 + \frac {3}{2}}$ $t = -…
S4M1R
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Finding the other $x$-intecept of a quadratic equation $ax^2+bx+c=0$ when $a$ is unknown and one $x$-intercept is known

One of the $x$-intercepts of the function $f(x)=ax^2-3x+1$ is at $x=-1$. Determine $a$ and the other $x$-intercept. I happen to know that $a=-4$ and the other $x$-intercept is at $x=\frac{1}{4}$ but I don't know how to get there. I tried…
Helix
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If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$ My Procedure The roots are $$\frac{-b+\sqrt{b^{2}-4ac}}{2a}$$ and $$\frac{-b-\sqrt{b^{2}-4ac}}{2a}$$ $\therefore$ the roots are…
user173094
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