# Tagged Questions

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

2answers
523 views

### If $ax^2+bx+c=0$ and $2x^2 +3x+4=0$ have a common root where $a,b,c \in \Bbb N$,find least value of $a+b+c$

Problem: If $ax^2+bx+c=0$ and $2x^2 +3x+4=0$ have a common root where $a,b,c \in \Bbb N$, find least value of $a+b+c$ Solution: Here $2x^2 +3x+4=0$ will give complex roots These roots will ...
3answers
120 views

### Show the roots of the quadratic equation $z^2 +bz+ c = 0$ lie in or on the unit circle

So I need a little help with the following: Considering separately the cases of real and complex roots show that the roots of the quadratic equation $z^2 +bz+ c = 0$ lie in or on the unit circle (i.e....
0answers
24 views

### Geometric interpretation of the coefficients of the quadratic equation.

The quadratic equation has three general forms: $ax^2+bx+c$ $a(x-r_1)(x-r_2)$ $a(x-h)^2+k$ $r_1$ and $r_2$ are the zeroes of the quadratic. $h$ is the horizontal position of the ...
4answers
67 views

### How do I find the solution(s) to my second-degree equation?

$$f(x) = x^2 - 3x$$ My attempt : \begin{align} x^2-3x &= 4\\ x(x-3) &= 4\\ x-3 &= 4 \\ x &= 7\\ \end{align} I managed to solve one part of this problem but that one part is ...
5answers
84 views

### When is $\sqrt{x/y^2}$ equal to $\sqrt{x}/y$?

The solution to the quadratics is given by $r = -\dfrac{b}{2a}\pm\sqrt{\dfrac{b^2-4ac}{4a^2}}$, which is shortened to $r = -\dfrac{b}{2a}\pm\dfrac{\sqrt{b^2-4ac}}{2a}$, but I'm wondering how if this ...
0answers
34 views

### Quadratic term answer fast please [on hold]

let k be a real number such that k≠0.if a and b are non zero complex numbers satisfying a+b=-2k and a²+b²=4k²-2k,then a quadratic equation having (a+b/a)and (a+b/b)as its roots is equal to
0answers
37 views

### Quadratic term answer fast [on hold]

let sin x and sign y be the roots of the quadratic equation a sin square theta + b sin theta + C is equal to zero,such that sin x + 2 Sin y is equal to 1 then the value of a square + 2bsquare + 3ab+ ...
2answers
45 views

### How to solve the following quadratic word problem given a quadratic equation?

The height of a ball(h), in feet, after s seconds is modeled by the equation $$h=-16t^2+40t-6$$ How many seconds does it take for the ball t reach its maximum height? First thing i did was turn the ...
2answers
40 views

1answer
19 views

### Find the range of values for k for which the equation $x^2+(a-2)x+(a+3)=0$ had no real roots

I don't understand the question at all. Find the range of values for a for which the equation $x^2+(a-2)x+(a+3)=0$ has no real roots.
3answers
46 views

### Why are the solutions of the equation different? : $x=2 => x^2=4 => x=±2$

If I define the variable $x$ as $x=2$, then $x^2=4$. But the solutions of $x^2=4$ are $±2$(two solutions). I defined what the variable $x$ is, then why are the solutions for the equation $x^2=4$ two, ...
1answer
86 views

### What technique reduces factorable ax^2+bx+c=0 to factorable where a=1

The normal way to factor ax^2+bx+c=0 is to look for t,u,v,w such that: (tx+u)(vx+w) = 0 so that tv=a, uw=c, and uv+wt=b. This can be tricky, since there can be several possibilities for t,u,v,w. ...
5answers
59 views

### On the equation $|x|^2+|x|-6=0$

Which of the following are true for $$|x|^2+|x|-6=0$$ 1. It has $4$ roots 2. The sum of the roots is $-1$ 3. The product of the roots is $-4$ 4. The product of the roots is $-6$ Only one of the ...
3answers
79 views

1answer
870 views

### How do I prove a quadratic is always positive or negative for x?

I looked this up and seen something that was beyond my A-Level Maths course. In class we are doing the discriminant and sketching quadratic graphs, so it is nothing advanced. My teacher completed ...
6answers
61 views

### How to solve without solving by inspection? $\frac{x+5}{x+k}=\frac{-kx+5}{x-1}$

Background: This is from a test review on functions. The original problem was Find the value of $k$ so that the function $f(x) = \frac{x+5}{x+k}$ will be its own inverse. I found the answer by ...
2answers
57 views

### Solve the quadratic equation

$$\sqrt{a-\sqrt{a+x}}=x$$ This equation contains one variable x we have to find the value of x.I tried to simplify it but it doesn't work....i have also tried the basic concepts of quadratics ...
2answers
799 views

### Optimization: maximum area of a triangle under a parabola

Optimization: maximum area of a triangle in a parabola Inside a curve ($x^2-25$ - Parabola) a triangle is drawn with A as the vertex at the origin and the line joining points B and C lie on the ...
2answers
44 views