Questions on quadratic equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-h)^2+k$ or $y=a(bx+c)(cx+d)$.

learn more… | top users | synonyms (1)

0
votes
1answer
35 views

Quadratic $y = -4.9x^2 + 25x$

Here is my questions, please help. In the game of foot, a team can score by kicking the ball over a bar and between two uprights. For a kick in a particular game, the height of the ball above the ...
0
votes
1answer
37 views

Wrong solution set in textbook, quadratic equation

So we have an the equation $\frac{2}{3}t^2+\frac{4}{3}t=\frac 15$, when you finish solving the equation you get $t = \frac{-10 + \sqrt{130}}{10} $ and $\frac{-10 - \sqrt{130}}{10}$. The text book ...
1
vote
2answers
31 views

Prove the given condition from given two quadratic equation

Question: If the quadratic equations $x^2+bx+c=0$ and $bx^2+cx+1=0$ have a common root then prove that either $b + c + 1 = 0$ or $b^2 + c^2 + 1 =bc + b + c$ Till yet, I had figured the common ...
1
vote
1answer
26 views

Checking some work on finding roots

OK, I have the following response function: $$H(\omega) = \frac{1-\omega^2 LC}{1+\omega^2 LC - i \omega RC}$$ I want to find where it becomes $\frac{1}{\sqrt{2}}$. This should be simple enough. ...
0
votes
1answer
37 views

Simplification of another nasty expression

I have the following condition $$ 2 \frac{x^2}{y^2} \left(1 - \frac{1}{y^2} \right)+ \frac{1}{y^2} \leq 1$$ Can anyone help me simplify it to the best possible relationship between $x$ and $y$?
0
votes
3answers
27 views

Solving Quadratic equation by factorizing

The question is 2x^2 - 7x + 3 = 0. First of all quadratic equation is written in the form of ax^2 + bx + c = 0 in where a,b and c are numbers. In this equation I was told to use the matrix method. ...
0
votes
1answer
21 views

Find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$

I'm trying to find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$ can take any real value. These are the steps I've taken so far: $$ xy + ky - x^2 - 3x = 0 $$ ...
0
votes
2answers
21 views

Find the range of $k$ in $f(x) = \frac{x^2-k}{x-2}$

I have the following question: For real $x$, $f(x) = \frac{x^2-k}{x-2}$ can take any real value. Find the range of values $k$ can take. Here is how I commenced: $$ y(x-2) = x^2-k \\ -x^2 + xy - ...
-1
votes
1answer
87 views

If the quadratic equation $x^2 + 2kx + 2(k + 4) = 0$ has distinct real roots, then $k^2 – 2k – 8 > 0$ [closed]

The quadratic equation $x^2 + 2kx + 2(k + 4) = 0$ has distinct real roots. Show that $k^2 – 2k – 8 > 0$. I'm not sure what you're meant to do here- it's a 2 mark question.
3
votes
1answer
65 views

Why doesn't this method of solution work?

Solve $$\sqrt{2x^2 - 7x + 1} - \sqrt{2x^2 - 9x + 4} = 1 \tag1$$ I tried to do the following: $$(2x^2 - 7x + 1) - (2x^2 - 9x + 4) = 2x-3\tag2$$ Dividing $(2)$ by $(1)$ yields $$\sqrt{2x^2 ...
-2
votes
2answers
42 views

Completing the square Quadratics

Solve this quadratic equation by completing the square: $2x^2+x-4=0$ Can I have the method aswell please.
0
votes
2answers
24 views

expanding and simplifying an expression

so the question is $(2x - 2)^2 + (3 - 2x)^2$. My working out: $$ 2x (3 - 2x)^2 + 2 (3 - 2x)^2 = 6x^2 - 4x + 6 - 4x = 2x^2 - 4x + 6. $$ I was a bit confused as their was another way to work out this ...
0
votes
1answer
27 views

Expand and simplify

I've removed the brackets from the first equation in where it is 5a^2 + 2a - 5 and then multiplied 3 to the numbers inside the bracket. But I'm not sure what steps to take after that. (5a^2 + 2a - 5) ...
0
votes
2answers
36 views

Solving quadratic equations in the field $F_5$

Let $y = x^2 + 2x + 2 = 0$. Solve the equation in the field $F_5$. So I used the common $b^2 - 4ac$ formula and got that $x$ is either $-1/2$ or $-3/2$ but I'm not sure if this is in the field...
0
votes
1answer
34 views

factor polynomial as $(1-x\phi)(1+x\phi)$ instead of $(x-\phi)(x+\phi)$

I'm reading Generatingfunctionology, which is turning into a bit of an algebra review for me, and I am stumped by a step on page 9. I see the quadratic $1-x-x^2$ and I just pull the minus out ...
1
vote
1answer
36 views

Deriving coefficient q in reduced quadratic equation using Vieta's formulas

I have the following example of the use of Vieta's formulas in my textbook: Let's have a quadratic equation of the form $x^2+x+q=0$ The following conditions apply: the equation has two roots, such ...
2
votes
0answers
48 views

$A(x+p)²-B(x-p)²=y$, historical/math reference

I'm trying to build a reminder of all that I found about the quadratic function over the years. Here I came across this form of quadratic equation that I did not know: A(x+p)²-B(x-p)²=y I have no ...
0
votes
2answers
42 views

Basis for the Space of Quadratic Polynomials $P^{(2)}$ — Homework Help

Prove that $1+t^2$, $t+t^2$, $1+2t+t^2$ is a basis for the space of quadratic polynomials $P^{(2)}$. I have worked it out to the point where I have the following: $(1+t^2)(1, 0, 1)^T ...
0
votes
1answer
21 views

Application of the Rational Roots Theorem

Let f(x)=3x$^3$ - 40x$^2$ + 97x + 10 a. Find a rational number r such that f(r) = 0. (Hint: Use the rational roots theorem to narrow down possibilities for r.) So, I figured this part out. write r ...
2
votes
0answers
29 views

can someone break this quad formula down for me?

Can someone explain how this person yield the stuff on the right side using quad formula?
0
votes
4answers
36 views

After completing the square.

After completing the square, what are the solutions to the quadratic equation below? $$x^2 + 2x = 25$$ Honstely I think it's B. But I'm not sure.
0
votes
1answer
61 views

Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$

I'm working through the book Core Maths for Advanced Level on my own, and, after solving the above problem, I'm not getting the same answer as the book. So, given: $$x^2 + ax + a^2 = 0$$ Using the ...
1
vote
2answers
36 views

Solve the equation, find the x

I need to find the x in thid equation. How is it done? a = x+1/x I've tried turning it into x² = 1-x times a, but it's not a system.. so.. any ideas?
0
votes
1answer
38 views

Parabola - How far from the thrower does the ball strike the ground?

The height of a ball thrown in the air is given by $h(x) = \frac {–1}{12} x^2 + 6x+ 3$, where x is the horizontal distance in feet from the point at which the ball is thrown. c. How far from the ...
0
votes
1answer
46 views

Find the dimensions of a square piece of cardboard given data of it folded into a square (cubic inches, etc.)

A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in. squares out of each corner and folding up the sides. The box needs to hold 1000 in3 . How big a ...
0
votes
2answers
81 views
0
votes
0answers
65 views

Quadratic Formula: Box, Word Problem.

An open-topped box is being made from a piece of cardboard measuring 12 in. by 30 in. The sides of the box are formed when four congruent squares are cut from the corners, as shown in the diagram. The ...
1
vote
1answer
27 views

Quadratic Formula: Word Problem.

A person decides to build a horse corral using a barn for one side. Has has 30m of fencing materials and wants the corral to have an area of 100m^2. What are the dimensions of the corral? Let width ...
1
vote
3answers
49 views

Under what conditions will one solution of $ax^2+bx+c = 0$ be the reciprocal of the other?

Under what conditions will one solution of $ax^2+bx+c = 0$ be the reciprocal of the other?
0
votes
2answers
72 views

Quadratic equations word problem.

A uniform walkway is built around a rectangular flower bed that is 20m by 40m. There is enough material to make a walkway that has a total area of 700 m^2. What is the width of the walkway? I need ...
0
votes
0answers
11 views

parabolic function

The main structure of the Hale Street Bridge, being constructed across the Brisbane river, is a parabolic arched bridge with a span of 60 meters. The maximum height of the arch above water level must ...
2
votes
1answer
36 views

is the sum of roots of a quadratic with rational coefficients always rational

quadratic is $ax^2 + bx +c = 0$ let the roots be $f$ and $g$ as $f + g = -\frac{b}{a}\ $ and $\ f \cdot g = \frac{c}{a}$ does this imply if a quadratic has rational coefficients the sum of the ...
7
votes
1answer
99 views

Coincidence? : $d(ax^2+bx+c)/dx=\pm \sqrt{\Delta}$

As the title says, is it just a coincidence that $d(ax^2+bx+c)/dx=\pm \sqrt{\Delta}$? (where $\Delta=b^2-4ac$, i.e. discriminant of the quadratic). We can get this easily from rearranging the ...
0
votes
1answer
32 views

For which values of $n$, the real part of the $n$-th root of unity is a quadratic irrational?

For which values of $n$, the real part of the $n$-th root of unity is a quadratic irrational? That is, when is it a root of a quadratic polynomial with integer coefficients? I believe that the answer ...
0
votes
1answer
23 views

Can you simplify a coordinate

Can you simplify $(-6,-36)$ to $(-1,-6)$ if the first coordinate is the min value of a quadratic graph. The equation is $y = x^2 + 12x$.
0
votes
1answer
99 views

Solving an equation involving factorial notation

I was given this problem in the text book: $$\frac{(n+4)!}{(n+2)!} = 6$$ $$n \in I $$ Since the textbook doesn't have the solution, I'm wondering if I'm right: $$\frac{(n+4)!}{(n+2)!} \Rightarrow ...
1
vote
1answer
30 views

Sum of $n^{\text{th}}$ powers of roots of quadratic

How would I go about finding an expression (preferably closed form) for the sum of $\alpha^n+\beta^n$ in terms of $\alpha + \beta$ and $\alpha\beta$ (where $\alpha$ and $\beta$ are the roots of a ...
2
votes
2answers
29 views

Equation with two unknowns

I have this equation to solve and I solved it but don't know if the result is correct. $\begin{cases}2\pi r_1+2\pi r_2=24 & (1) \\ \pi r_1^2+\pi r_2^2=20 & (2)\end{cases}$ Equation $(1)$ ...
1
vote
1answer
42 views

Quadratic Functions Word Problem

A holding pen is being built alongside a long building. The pen requires only three fenced sides, with the building forming the fourth side. There is enough material for 90m of fencing. Predict what ...
0
votes
1answer
38 views

solve an quadratic equation

I was reading a document , where I stucked in figuring out this equation. $f(k)= k^2-nk+\frac{n^2 - n}{2}$. This is a quadratic function of $k$. It is minimized when $k=\frac{n}{2}$ (the $k$ ...
2
votes
2answers
85 views

Find the value of $f(x)$ for $x = 2 + 2^{2/3} + 2^{1/3}$

If $x = 2 + 2^{2/3} + 2^{1/3}$, then find the value of $f(x)=x^3 - 6x^2 + 6x$. I am unable to get to the answer - end up with more than one term. Please help me solve this!
1
vote
1answer
50 views

For the given quadratic equation find the value of p

For the equation 3x^2 + px + 3 = 0 , p>0, if one of the roots is square of the other, then p is equal to? Solving the equation, i get the value of p as -6 but the question states that p>0. Is there ...
0
votes
2answers
22 views

Quadratic Function: X intercepts.

A quadratic function with a y-intercept of 0 and an axis of symmetry of x=-1. Apparently, there is suppose to be 2 x-intercepts, which I really don't understand. How can the parabola cross the x ...
0
votes
2answers
36 views

Quadratic Functions word problem.

I have the quadratic function $$y=\frac{1}{294}(x-84)^2-24$$ that represents the shape of the cables of a certain bridge. I am suppose to be determining the vertical height of the cables above the ...
2
votes
1answer
45 views

What is the spherical parametrization of an ellipsoid NOT centered in the origin?

I would like to know how to parametrize an ellipsoid not centered in the origin, but with its axes parallel to the main axes of the reference system. The result I am looking for would be an ...
0
votes
2answers
41 views

Quadratic Functions Problem

Question: The main section of a certain bridge has cables in the shape of a parabola. Suppose that the points on the tops of the towers where the cables are attached are 168m apart and 24 vertically ...
1
vote
5answers
65 views

For what real number $c$, this equation has exactly three solutions?

For what real number c does the equation $|x^2 + 12x + 34| = c$ has exactly three solutions?
0
votes
3answers
56 views

Finding dimensions using quadratic formula

A 52 m long fence is constructed on three sides of a housing block with area 240 m^2. The fourth side facing the road is left open. Find the dimensions of the block. Also here's another question I ...
0
votes
3answers
27 views

Problem Solving quadratics

A rectangular paddock has perimeter of 600 m and area 21 600 m^2. Find the dimensions of the paddock. So far, I've figured out the formula is x(300-x)=21600 and rearranged to 300x-x^2=21600. I'm not ...
1
vote
1answer
31 views

Quadratics: Solve for B and C.

If I know that the points (-1,6) and (2,3) are on the graph of the quadratic function f(x) = 2x^2 + bx + c, how do I determine b and c? Thanks to anyone who helps.