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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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Finding possible quadratic equations given conditions of their roots

I have an issue with the following problem: Two quadratic equations have real roots $\alpha$ and $\beta$ such that $$\alpha - \beta = 3$$ and $$\alpha \beta = 2(\alpha + \beta).$$ Find the two possible quadratic equations that satisfy these…
sangstar
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Multiplied X in Quadratic Equation - Delta always lower than 0

I'm new to Quadratic Equations and I am following the two formulas to find $x_1$ and $x_2$ and they are: $\Delta = b^2 - 4ac$ $x = \dfrac{-(b) \pm \sqrt\Delta}{2a}$ but delta always gives a negative number; for example I have the following…
Feelsbadman
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Forming a quadratic equation with the given roots

Question: If $\frac{p^2}{q}$ and $\frac{q^2}{p}$ are the roots of the equation $2x^2+7x-4=0$, find the equation whose roots are $p$ and $q$($p+q$ is real). My attempt: The required equation is…
MrAP
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Vertex of a parabola

A simple task, we throw a ball into the air upwards as vertically as possible and record the height of the ball at release, $(height=1m, time = 0)$, and the time the ball hit the ground. $(height=0, time=2.80s)$. We are trying to solve the equation…
Stack
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Initial velocity of a ball which is thrown

Question: A ball is thrown straight up, from $3\rm m$ above the ground, with a velocity of $14\rm m/s$. When does it hit the ground? In this question, to find the total height first, we must also take into consideration the acceleration due to…
user34782
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Quadratic equation?

Say I have an equation, $\sqrt 2 x^2 - \sqrt 3 x + k = 0$, $k$ is a constant and there are 2 solutions $\sin \theta$ and $\cos\theta$ in the interval $0\le \theta \le \pi/2$. What is the value of $k$? How should I view this question? Equaling two…
cartmanbrahhhhh
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Solving for $x$ in Quadratic Equations

So, I have finished study for linear equations for my methods course but now I have run into a problematic quadratic equation. I have tried researching for a method of tackling this question but I have come up with nothing. I have played around a…
Chet Power
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Looking for a quicker way to solve a quadratic problem

Let $f(x) = x^2 – 6x + 3$ and $g(x) = k – f(1 – x)$ for some constant $k$. It is known that $y = g(x)$ touches x-axis at only one point $B = (b, 0)$. (i) Find the values of $b$ and $k$. (ii) Solve $2f(x) + g(x) – 2 = 0$. My attempt:- $g(x) = k –…
Mick
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The equation $a^x +a^{-x}=b$

Given $a$ is a fixed real number that is greater than one, how many real numbers $b$ are there such that the equation $^{x} + a^{-x} = $ has a unique real solution x? To solve this problem, I tried to plug in $a = 3$. So, I want to find how many…
Cyclopropane
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Simultaneous equation that turns into quadratic

Solve for $x$ and $y$: \begin{cases} y &= 4x^2 - x - 6 \\ y &= 2 - x. \end{cases} I have tried rearranging to get $x + y = 2$ and then substituting $y$ into it but hit a dead end. I'm pretty sure it turns into a quadratic equation. Any help would be…
L Smith
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What are the values of $k$ when $kx^2+x+k$, has equal zeroes?

Show that the quadratic equation $kx^2 + 2(x+1)=k$ has real roots for all the values of $k\in \mathbb{R}$ what i did $kx^2+2x+2-k=0$ $4-4(2-k)(k)>0$ $4-8k+4k^2>0$ $(64±64)÷ 4(2)>0$ $128÷ 8>0$ $16>0$ please help me check
john
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Given the quadratic equation $p(x^2 +9)= -5qx$ has two equal roots, find the ratio of $p:q$. Hence, solve the quadratic equation

Given the quadratic equation $p(x^2 +9)= -5qx$ has two equal roots, find the ratio of p:q. Hence, solve the quadratic equation so this is what i got so far : $$px^2+9p+5qx=0$$ $$(5q)^2 - 4(p)(9p)=0$$ $$25q^2 - 36p^2 =0$$ $$(5^2 q^2) - (6^2…
bryan
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Why was this answer incorrect?

This question appeared in my homework, and we went over it in class today. Solve the Zeros: $$3x^2 = -81$$ My solution: $$3x^2=-81\\3x=\pm9i\\x=\pm3i$$ Correct…
Travis
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Is there a general formula for a quadratic that is always positive?

I encountered a problem of quadratic. It asks for a quadratic that is in the form $f(x)=ax^2+bx+c$. It is always positive and $b$ is greater than $a$. Than it asks me to find $f(17)$ based on $f(16)=20$. Is there a fast and easy way to do this? My…
M. Chen
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how do I solve this quadratic equation with a fraction?

I seem to have trouble with quadratic equations when it comes to fractions and square roots. $$ \frac{1}{x}+2x=3 $$ How do I solve this equation?
Brendan Jackson
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