Tagged Questions
1
vote
1answer
25 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
2answers
44 views
help with my hw its a quadratic equation [closed]
Write the quadratic equation using the following factor
$(7x-3) (-2x+1)$
$(R+9) (R-9)$
Factor: $x^2+6x+9$
Please help the hw is due tommorow
1
vote
1answer
53 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
87 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.
0
votes
2answers
82 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 ...
3
votes
1answer
52 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
32 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
128 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
207 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
73 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
133 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
92 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 ...
6
votes
6answers
242 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
38 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
38 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
152 views
Definition of quadratic equation?
What is a quadratic equation and what is its simplified and cannonic form?
1
vote
3answers
195 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
212 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 ...
1
vote
3answers
93 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
238 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 ...
