Mathematics Stack Exchange
Mathematics Stack Exchange

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
-1
votes
2 answers

Find the quadratic equation whose roots are $(q+n)$ and $(p+m)$?

If $p$ and $q$ are the roots of equation $x^2+mx+n=0$ and $m$ and $n$ are the roots of equation $x^2+px+q=0$ then the equation whose roots are $(q+n)$ and $(p+m)$ is $A) \; x^2-4$ $B) \; x^2-2x+4 $ $C) \; x^2+4x-4 $ $D) \; x^2+2x-8 $ Note that $p,…
Sumit Jha
  • 153
-1
votes
1 answer

Quadratic Equation - Prove the following

If $c$ is positive and $2ax^2 + 3bx + 5c$ does not have any real roots, then prove that $2a - 3b + 5c > 0$.
user406945
  • 3
  • 4
-1
votes
3 answers

$x^2+px+q=0$ where $p+q=2017$, find integers only $x_1$ and $x_2$

Using a program I found one pair only x1=-1 x2=-1008, maybe there are more, but I need a step by step mathematical solution.
user410918
  • 77
  • 6
-1
votes
4 answers

Why do these two methods of 'solving' output different solutions?

We were putting equations into vertex form to factor as part of solving, and we were told to use the equation $c=\left(\frac{b}{2}\right)^2$. I figured you could skip vertex form and factor more easily using $c=b^2$. These two solving methods gave…
Travis
  • 3,396
  • 6
  • 23
  • 44
-1
votes
1 answer

Equations Value of M one given Root

The question I have is 2x^2+mx-21=0. The area I am stuck on is finding one of the roots, one root was given as -7, however I need to find the other one.
Nicole Carr
  • 21
-1
votes
1 answer

The question states that the roots can only be imaginary but I think they are equal too

Question Statement:- If $p,q,r$ be in H.P. and $p$ and $r$ are of same sign, prove that the roots of the equation $px^2+2qx+r=0$ will be imaginary. My solution:- As $p,q,r$ are in H.P. then the relation b/w the three is as…
user350331
  • 2,728
  • 4
  • 20
  • 41
-1
votes
1 answer

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.
tommen
  • 3
  • 1
-1
votes
1 answer

How to solve something like $x^2 + \sqrt{2}\,x - 3$?

What is exactly the MO when it comes to solving a quadratic equation like $x^2 + \sqrt{2}\,x - 3$? Do I take the part with the under root to the other side and end up with $x^4$?
IncorrigiblePenguin
  • 7
-1
votes
1 answer

How to expand a equation into a quadratic equation?

I need a explanation and steps how I can expand this equation: $$(x−p)^2+(mx+c−q)^2=r$$ into this one: $$(m^2+1)x^2+2(mc−mq−p)x+(q^2−r+p^2−2cq+c^2)=0$$ Thank you for your time.
BabaMara
  • 3
-1
votes
2 answers

Express $s = -5t^2 + 40t$ in the form of $a(t-b)^2 + c$, where $a$, $b$ and $c$ are the constants.

$s= -5t^2+ 40t$. Express $s$ in the form of $a(t-b)^2 + c$, where $a$, $b$ and $c$ are the constants. $s = -5t(t-8)$. I have factorized it.
Jeannine
  • 1
  • 1
-1
votes
2 answers

the result after exploding second degree equation

Why is $$(1+x+x^2)^2 = 1+x^2+(x^2)^2+2(x+x^2+x^3)?$$ My professor wrote that in the class but he didn't explain why. Thank you
zeeks
  • 241
-1
votes
1 answer

how to solve this : $R(m)=12+5m -0.4m^2$?

How to solve this : $R(m)=12+5m-0.4m^2$? Jeremy's junkers keeps track of the revenue it makes from selling used exhaust manifolds. they have found that the revenue is a function of the number sold and this can be modeled by the quadratic function,…
rejeana Hayes
  • 1
-1
votes
2 answers

Find equation of a line intersecting parabola at one point only?

Find equation of a line with gradient equal to $2$ which intersects the parabola $y = 6 − x − x^2$ at one point? I tried using the equation of the line $y=2x+c$ and making it equal to $y= -x^2 - x +6$. Then finding $x$ using the quadratic formula.…
Dzoker
  • 11
  • 1
  • 2
  • 4
-1
votes
1 answer

Using a number system other than the decimal

Travelling in the Kingdom of Crystal Skull, Indiana Jones discovered a small box with notation $$ 3 x^2 - 25 x + 66 = 0 \implies x_1 = 4,\; x_2 = 9, $$ which seems to be incorrect. However after some reflection he realised a number system other…
Carli
  • 43
-2
votes
1 answer

List the elements of the set $\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$

I don't get this maths equation Can anybody explain it ? Thanks List the elements of the following set: $A=\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$.
X123
  • 1
1 2 3
…
64 65