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
vote
1 answer

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.
Dan
  • 15
1
vote
3 answers

Consider a quadratic equation

$x^2-2(a+1)x+3a+2=0$ Where a is any real number. Find all values of a so that the equation has two distinct real roots. I tried solving for a by using the inequality $b^2-4ac\gt0$... but when i substitute the value into the equation and input it…
mathemator
  • 111
1
vote
2 answers

How to Find The Roots of this Quadratic Given Sum & Product

My question is: The sum of the roots of a quadratic is $55/72$, and the products of the roots is $-25/12$. Find the roots. How I'm trying to do it so far: (Also, please correct my thought process if it's wrong. I really want to become better at…
user164403
  • 939
1
vote
1 answer

What's wrong with my accelerated motion equations?

I'm trying to solve these accelerated motion equations for velocity but I'm getting strange solutions with lower final velocities when using higher initial velocities, which doesn't make sense to me since acceleration is positive. I can't figure out…
ecv
  • 113
1
vote
4 answers

finding an quadratic equation by the roots & another equation?

I am new to this site & doesn't know any rules & regulations. So sorry if I am doing any mistake. the question is stated as follows. I. $\alpha$ and $\beta$ are the roots of the equation $x^2 + bx + c = 0$. find the quadratic equation in terms of…
Pawan Vimukthi
  • 21
1
vote
3 answers

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, step by step if you can. How do I figure this out? I…
Simon
  • 33
1
vote
1 answer

When is $(x+3)^2$ equal to $x^2 +9$?

https://matheducators.stackexchange.com/a/1400/775 Someone commented that the equation in the above answer might sometimes be correct after I commented a correction (feel free to rewrite it appropriately in the question title, my phone does not have…
Nzall
  • 125
1
vote
4 answers

Finding the two digit number.

A two digit number is such that the product of its digit is 18.When 63 is subtracted from the number , the digits interchange their places.Find the number.
Snehil Sinha
  • 1,179
1
vote
3 answers

Determine the value(s) of the ratio $x:y$ if $2x^2-xy-3y^2 = 0$

I was asked to determine the value(s) of the ratio $x:y$ if $2x^2-xy-3y^2 = 0$. I didn't know what this meant, so I just solved the equation to get $x = -y$ or $x = \frac{3}{2}y$. What does the question mean?
Aspiring Mathlete
  • 2,312
1
vote
1 answer

What will be the nature of the roots of the equation?

What will be the nature of the roots of the equation $7x^2 – 2x + 3 = 0$ If I have two options like Imaginary and complex. Are both options are valid? Or more near answer is Imaginary. In my book it is written as if Discriminate is less than $0$…
zonnie
  • 135
1
vote
3 answers

How to invert these equations

Apologies in advance as maths has never been my strong point (I'm not even sure which tag to use). I'm developing some software that uses some equations to convert values being read from a hardware device. There are three variations, each with a…
Andrew Stephens
  • 113
1
vote
1 answer

Isolate "a" in a quadratic function

You have a quadratic function: $ax^2 + bx + c = y$. If you know $b$ and $c$, are able to plug any domain value $x$ into this blackbox equation and receive a range value $y$, and do not know the vertex of the equation, how could you find the unknown…
Paul T.
  • 13
1
vote
2 answers

Prove that $g(x) > 0$

If $f(x)$ is a quadratic expression such that $f(x) > 0,\ x\in\mathbb{R}$ and if $g(x)= f(x) + f'(x) + f''(x)$, then prove that $g(x) > 0, \ x\in\mathbb{R}$.
user142778
  • 61
1
vote
1 answer

Quadratic expression

If $$\frac{a_0}{n+1}+\frac{a_1}{n}+\frac{a_2}{n-1}+\ldots+\frac{a_{n-1}}{2}+a_{n}=0,$$ then the maximum possible number of roots of the equation $${a_0}{x^n}+{a_1}{x^{n-1}}+{a_2}{x^{n-2}}+\ldots+{a_{n-1}}{x}+{a_n}=0$$ in $(0,1)$ will be...? This…
sammy2014
  • 11
1
vote
2 answers

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
Adma
  • 41
1 2 3
…
64 65