1
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1answer
38 views

Quadratics Word Problem

The path of a football flying through the air can be modelled by a quadratic equation. The football reaches the ground after 12 seconds in flight and is kicked from a height of 1 meter. The parabola ...
1
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3answers
32 views

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions?

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions? Equation: $$0 = 3x^2 + tx + 10$$ Can you please explain the answer in simple terms, ...
1
vote
3answers
40 views

How do I solve: $6(x^2+2)<17x$

How do I solve this kinds of inequality. I can do it if all the 'x' is in one side. However, this one have x at both sides of the equation. And we don't know whether it's a positive or negative value. ...
0
votes
3answers
35 views

Quadratics with unknowns

If $5x^2 – t = 4x$, and $x$ and $t$ are both positive real numbers. What is $x$ equal to? How do you find $x$? Is there a specific formula?
0
votes
1answer
71 views

Find pressure in a sinusoidal function

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with laughing gas. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 ...
1
vote
2answers
33 views

Analytical approach to a quadratics problem

I'm a bit rusty on functions and this exercise got me thinking quite a bit. The function $y=x$ is tangent to the graph of a certain $g$ function in $x=0$. Function $g$ can be defined as: ...
0
votes
3answers
38 views

Find the set of real numbers ($x$ not equal to zero) such that $2x + 1/x < 3$.

Pretty straightforward question, I just had a question for the conclusion. I rearranged, and factored and have the quadratic: $$2x + 1/x < 3$$ (multiply both sides by x and rearrange) $$2x^x - ...
1
vote
2answers
55 views

Solve $f(x) = ax^2 + bx + c$ to find the value of $K$

$f(x)=ax^2+bx+c$, where $a=-9$, $b=12$ and $c=16$. If $$-1<f'(x)<1$$ then $h<x<k$. To $2$ decimal places, what is the value of $k$? Hi, this is working for solving $f(x) = ax^2 + bx + ...
0
votes
1answer
44 views

Determining quadratic function of this word problem

I have this word problem in my homework: ...
0
votes
2answers
126 views

How would I solve the quadratic $x^2+3x-70=0$?

How would I solve the following quadratic equation $$x^2+3x-70=0 $$ This is my attempt below $$(x-7x) (x+10x)=0 $$ $$ x-7x=0 \implies -6x=0 \implies x=6$$ $$x+10x=0 \implies 11x=0 \implies ...
1
vote
5answers
32 views

Linear systems from positions a quadratic passes through?

I don't understand the question. $$y = ax^2 + bx + c$$ passes through the points $(1,-4),(-1,0),(2,3)$. Write down a linear system (unknowns $a,b,c$) of three equations relating the unknowns to each ...
0
votes
0answers
47 views

Given the matrix, find c such that det(D)=0 has a repeated solution

Given the matrix $D= \begin{vmatrix} 1 & x & x^2\\ 2 & c & 4\\ 3 & 2 & 1 \end{vmatrix} $ Find c such that $\det(D)=0$ has a repeated solution for $x\in R$. I got up to ...
-3
votes
1answer
94 views

To find ? in equation $a^2+?^2=c$

How can we solve for $?$ in the below given Equation: $$a^2+?^2=c$$ I don§t want to use Square or Square root as the the number can be in decimals.
3
votes
5answers
1k views

Condition for a common root in two given quadratic equations

If $a,\;b,\;c$ are in Geometric Progression, then the equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root if $\;\displaystyle\frac da,\;\frac eb,\;\frac fc$ are in: Arithmetic Progression ...
0
votes
5answers
69 views

$x^2+y^2=1, 5x+12y+13=0$ Simultaneous Equations

Can someone solve this for me and show working out? I just can't do it and I don't know why I am getting x and y wrong. It will be very much appreciated. As basic as possible as well please.
1
vote
1answer
44 views

“Alternative factorising method” for quadratics not working

In class my teacher showed us an alternative method for factorising quadratics which are more awkward (i.e. the $a$ in $ax^2+bx+c$ is greater than 1). The method is: 1. Take your quadratic (e.g. ...
2
votes
1answer
56 views

Mechanics - Homework

A stone is thrown vertically down from a high building with an initial velocity of $4\;\mathrm ms^{-1}$. Calculate the time required for the stone to travel $30\;\mathrm m$. So far I have tried using ...
0
votes
1answer
90 views

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 ...
2
votes
3answers
102 views

If $a$ and $b$ are the zeroes of $x^2 + ax + b = 0$, then how many pairs of $(a,b)$ exist?

If $a$ and $b$ are the zeroes of $x^2 + ax + b = 0$, then how many pairs of $(a,b)$ exist? One Two Three Infinitely many Also, what are these pairs?
2
votes
3answers
99 views

Prove that for real numbers $x$, if $x^2 - 5x + 4 \ge 0$, then either $x \le 1$ or $x \ge 4$.

Its another homework question that I'm having trouble understanding. The full question is write a detailed structured proof that uses a proof by cases to prove that for real numbers $x$, if $x^2 - 5x ...
2
votes
3answers
86 views

Quadratic equation problems

There is a circle with a radius of $25$ ft and origin at $(0, 0)$ and a line segment from (0, -31) to (-37, 8). Find the intersections of the line and circle. I am asking for somebody to analyze ...
3
votes
2answers
12k views

Quadratic equation - Alpha and Beta Roots

If α and β are the roots of the equation x² + 8x - 5 = 0, find the quadratic equation whose roots are α/β and β/α. My working out so far: I know that α+β = -8 and αβ = -5 (from the roots) and then i ...
2
votes
0answers
99 views

Proving an equality involving binomial coefficients and summations

Question: $$\sum_{k=0}^{n}\left ( -1 \right )^{k}\binom{2n}{k}\binom{2n-k}{2n-2k}=\sum_{2n}^{k=0}\binom{2n}{k}^{2}\left ( \frac{1+\sqrt{5}}{2} \right )^{2n-k}\left ( \frac{1-\sqrt{5}}{2} \right ...
1
vote
1answer
87 views

Satisfying a condition on given quadratic equation

Let $P(x) = x^2 +2bx + c$ be a quadratic form where $b,c$ are real numbers.If $b^2 < c$ , show that $P(x) > 0$ for all $x$ .Is the converse also true? The value of $x$ after solving the ...
1
vote
1answer
67 views

How to show $\frac{300}{v} - \frac{300}{v+20} = 1.25$

A man travels a distance of $300$ km. On his return journey his average speed increased by $20$ km/h and his journey time decreased by $1\frac{1}{4}$ hours. If $v$ is the average speed of his outward ...
-2
votes
3answers
262 views

Determine the of p and other roots.

One of the roots of $3x^2 + p =5x$, is $2$. Determine the value of $p$ and the other root.
1
vote
2answers
99 views

jenny farm and the dozen egg ???

Farmer Jenny decides to expand her business interests and starts to package and sell the eggs produced by her chooks to a local shop. The cost of producing $x$ dozen eggs per day is given by, in ...
2
votes
1answer
57 views

Least value of $a$ for which at least one solution exists?

What is the least value of $a$ for which $$\frac{4}{\sin(x)}+\frac{1}{1-\sin(x)}=a$$ has atleast one solution in the interval $(0,\frac{\pi}{2})$? I first calculate $f'(x)$ and put it equal to $0$ to ...
0
votes
1answer
98 views

When finding the dilation factor of $y = 3(2x - 3)^2 - \frac{1}{4}$, why must the brackets be expanded?

When finding the dilation factor of $y = 3(2x - 3)^2 - \frac{1}{4}$, why must the brackets be expanded? Why can't the outside factor of $3$ simply be used for the dilation factor from the ...
2
votes
2answers
1k views

Find value of $k$ for which the equation has real roots

What can be the value of $k$ for which the equation $9x^2+2kx-1=0$ has real roots? Things should be known When the quadratic equation has real roots, then $d=b^2-4ac \ge 0$ . Where ...
4
votes
1answer
614 views

Relationship Between Roots and Coefficients of a Quadratic

To prove this lemma I use the relationship between roots and coefficients of a quadratic equation but did not get the result. Please help me prove this lemma. If ‎‎ $ - ‎\theta‎‎_{2}x^2 - ‎ ...
0
votes
1answer
121 views

Identifying Quadratic equations from collected information

A girl can row her boat at $5 km/h$ in still water. If she takes $1$ hour more to row the boat $5.2 km$ upstream then to return downstream, find the speed of the stream. What I had done so far: Let, ...
0
votes
1answer
563 views

Right Triangle Hypotenuse in a right triangle (Quadratic Equation)

The hypotenuse of a right triangle is $5 m$ if the smaller is doubles and longer is triples the new hypotenuse is $6\sqrt{5} m$. FInd the sides of the triangle. What I found so far: After coming up ...
-1
votes
2answers
120 views

Quadratic Equation Problem

A car covers distance of 1592cm. The number of hours taken for the journey is 1 half the number representing the speed in km/h. Find the time taken to cover distance. Hint: We will have to use the ...
7
votes
6answers
355 views

Solve $5a^2 - 4ab - b^2 + 9 = 0$, $ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0$

Solve $\left\{\begin{matrix} 5a^2 - 4ab - b^2 + 9 = 0\\ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0. \end{matrix}\right.$ I know that we can use quadratic equation twice, but then we'll get some ...
1
vote
2answers
48 views

How do I transform the equation based on the condition?

If $q$ and $w$ are the roots of the equation $$2x^2-px+7=0$$ Then $q/w$ is a root of ? P.s:- It is an another question of How do I transform the equation based on this condition?
2
votes
1answer
44 views

How do I transform the equation based on this condition?

If a and b are the roots of the equation $$2x^2-px+7=0$$ Then a-b is a root of ?
0
votes
2answers
346 views

Definition of quadratic equation?

What is a quadratic equation and what is its simplified and cannonic form?
1
vote
3answers
390 views

Changing from quadratic formula to standard form.

The graph of a quadratic function has $x$-intercepts $-1$ and $3$ and a range consisting of all numbers less than or equal to $4$. Determine an expression for the function. This is my problem. I ...
5
votes
4answers
553 views

find the least a, for which two equations have a common root

Could you help me out please. I have two equations: $2x^2-3x+1=0 $ and $ 2x^2-(a+3)x+3a=0$ I need to find the least $a$ for which these two equations have a common root. At a first glance I thought ...
2
votes
3answers
117 views

How to find orignal equations of type $y=ax^2+bx+c$. given 3 coordinate points?

Ok, simple question, having trouble understanding this in school. So given a set of 3 points (xy-plane), such as (40,30) (60,28) (20,25) i have to find the equation of the parabola. I ...
5
votes
3answers
240 views

What are a , b and c?

$$y = ax^2 + bx + c$$ which is tangent at the origin with the line $y=x$, It is also tangential with the line $y=2x + 3$. Determine the function! Draw a figure! My main question is this solvable? I ...