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
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Solve: Consider $f (x) = 90x^2 + 20x + 1$ then sum of digits of $f (111111)$ is...?

This is the question asked in my maths paper of quadratic equations but I am unable to understand which concept will be used here . Please help me in this.
Shinobi
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How to solve $16^x-10\cdot4^x+16=0$

I am unsure how to go about solving this equation to find x. Any help greatly appreciated.
Confused Student
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Least degree of polynomial equation

Find the least degree polynomial equation with rational coefficients whose roots is given $\sqrt2-1$ My book has given the solution as $x=(\sqrt2-1)$ $(x+1)^2 = 2$ I don't understand how this became the required polynomial equation.......I can't…
Abhinav
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What are quadratic functions and what are they for?

So, I have this page in my agenda that shows how to obtain the solution of a quadratic function. The solution for a quadratic equation in the form of $ax^2+bx+c=0$ can be found by using the quadratic formula: $x=\frac {-b\pm\sqrt {b^2-4ac}} {2a}$…
user558017
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3 answers

The polynomial has $a^2x^2+2(a+1)x+4$ exactly one root. What are the possible values for a?

The polynomial $a^2x^2+2(a+1)x+4$ has exactly one root. What are the possible values for a? I just want to know how to start.
Alexis Arias Pineda
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How do I show a quadratic in another form.

So I need to find $A$, $B$ and $C$ where: $A(x-1)(x+3) + B(x-1) + C$ is equivalent to $2x^2 + 12x + 7$. I know it has something to do with using alpha and beta but I don't know how to approach it. Help is very much appreciated. (Thank you this…
Mar
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Finding intersection between a quadratic equation and linear equation

Is it possible that you find a quadratic equation that NEVER intersects the linear equation y=x? I believe that it is impossible. I tried as many equations as I could such as y=(x+10)^2 and x=(y+10)^2, yet there seems to be none that do not…
user8068055
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How do I prove a quadratic expression to always be negative for all real values of x

So in school we are learning about quadratics. But I'm very confused on how to prove the question above. Example: $-x^{2}+x-2$ How would I prove that the expression is negative for all real values of x for expression above.
BobBobby
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A relation involving solutions of a quadratic equation

Consider the following quadratic equation: $$x^2 - (a + d) x + (a d - bc) = 0,$$ where $a, b, c, d \geq 0,$ and let $x_1 > 0, x_2 < 0$ be the solutions. I read in a book that since $$x^2 - (a + d) x + (a d - bc) = \Big[x - \frac{a + d}{2}\Big]^2 -…
g.pomegranate
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Prove the expression by using Quadratic equation's condition

One root of quadratic equation $a*x^2+b*x+c$ is square of another root. Then prove that $c*(a-b)^2 = (b^2-ac)*(a-b)$.
Partha Sarathi Das
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Is there any possible way to solve this equation with two different variables with different degrees?

$$649 + 96y = k^{2}$$ Also, $(y)$ or $(y + 1)$ or $(y-1)$ must be a perfect square. $y$ and $k$ are both natural numbers.
Aryaman Velampalli
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Quadratic equation with roots $\alpha$ and $\beta$

if $\alpha$, $\beta$ are the roots of the equation $ax^2 + bx + c = 0$, then the roots of the equation $a(2x+1)^2 + b(2x + 1) + c = 0$ are -
Anuraag Reddy
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Quadratic functions - using substitution

If $\alpha$ and $\beta$ are roots of the quadratic equation $ax^2+2bx+c=0$, find the quadratic equation with the roots $\alpha+\frac{1}{\alpha}$ and $\beta+\frac{1}{\beta}$ using transformation method or by substitution.
Isuru Madhushanka
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Sum of possible values of $n$

Find sum of possible values of $n$, where $n\in \mathbb{N}$,$x>0$ and $10
maverick
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$3+2i$ is one root of a quadratic function $f(x)=x^2+Ax+B$, where $A,B\in\Bbb R$. Compute the ordered pair $(A,B)$

In this question, I'm not exactly sure on how to solve this problem. Also, in $3+2i$, isn't there supposed to be a $x$. I understand that $i=\sqrt{-1}$. Please explain to me in a easy understandable way. I don't have much time, so please answer…
K.Enoch
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