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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 $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

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Nature of roots of $x^2+2(a-1)x+(a-5)=0$

A quadratic equation is given as $x^2+2(a-1)x+(a-5)=0$ then what could be the possible value of a if: a) The equation has positive roots b) The equation has roots of opposite sign c) The equation has negative roots I tried to check the nature of…
user220382
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What is the difference between the two real numbers that satisfy this equation?

What is the absolute difference between the two real numbers $x$ for which $(x+1)(x-1)(x-2) = (x+2)(x+3)(x-3)$? Express your answer in simplest radical form I tried guessing solutions but seeing how there are no common zeroes to both the left- and…
Puzzled417
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quadratic equation problem - proving a statement

I was given that $ax^2+2bx+c=0$ Using $y=x+\frac{1}{x}$ I need to prove that $acy^2+2b(c+a)y+(a-c)^2+4b^2=0$ Tried to make the pattern $x+\frac{1}{x}$ and to substitute $y$, but couldn't prove it.
Ramith Hettiarachchi
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Rewriting an algebraic equation with square roots

In as part of solving a question, the equation $a-3\sqrt a-4=0$ is written into $a^2-3a-4=0$ How is this done? Do you square everything in the equation? But in this case why are only the $a$ squared? Thanks!
Spica
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A polynomial problem related to lx^2 + nx + n

If the roots of $lx^2 + nx + n = 0$ are in the ratio $p:q$, find the value of $\sqrt{\frac{p}{q}}$ + $\sqrt{\frac{q}{p}}$ + $\sqrt{\frac{n}{l}}$. How to go about this problem?
Abhijith S. Raj
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Show that a quadratic function is always positive for all real values of $x$

How can I show that $x^2 +x +1$ is aways positive for all values of $x$? Do I use discriminant or completing the square?
user279584
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Finding condition for integral roots of a quadratic equation.

I need to find the values of k(possible) for which the quadratic equation $$x^2+2kx+k =0$$ will have integral roots. So I assumed roots to be $a,b$ Then I got the condition $a+b=-2k$and $a\cdot b=k$; so combining these I get $a+b+2ab=0$; And now I…
Freelancer
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Reducing equations to quadratic form

I have a chapter in my school course book on quadratic equations, in which we are learning how to solve nonquadratic-equations , by reducing them to quadratic form, the book describes 5 types of equations which can be solved by this method one of…
Batwayne
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Quadratic equation - possible values of k, coefficient of x

Need help on this question: If the roots of the quadratic equation $x^2 + kx - 18 = 0$ are integers, how many possible values of $k$ are there? Know it might be something to do with the discriminant, but can't figure out exactly what to do?
user256670
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discriminant of a quadratic function

Let $f$ and $g$ be a quadratic funtcions. Assume that $|f(x)|\geq |g(x)|$ for all $x\in\mathbb{R}$. How to show that $|d_f|\geq|d_g|$, where $d_h$ denote the discriminant of an arbitrary quadratic function $h$?
guilherme
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Write a quadratic equation in the form y=Ax^2 + Bx +C?

the question is to turn this question {1/4} double root to standard form. What i got is x = 1/4, x= 1/4 once you multiply them you get x^2 -1/2x -1/16 I think not sure if I'm correct and thanks to who ever it is that edits my question...i don't…
MATH ASKER
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Need help with tangents to a quadratic

The quadratic $y=kx^2+(3k-1)x-1$ and the straight line $y=(k+1)x-11$ meet. Find the range of value(s) of $k$ such that the line is a tangent to the curve. Got this question for school. Seems really simple and it's a non-calculator question but I'm…
gxv
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Proof related to quadratic equation

Suppose that m and n are integers such that both the quadratic equations $x^2 + mx − n = 0$ and $x^2 − mx + n = 0$ have integer roots. How to prove that n is divisible by 6?
user220382
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Solve $y^2 + 3xy - 10x^2 + y + 5x = 0$ for y in terms of x

I'm given the following equation: $y^2 + 3xy - 10x^2 + y + 5x = 0$ and asked to solve $y$ in terms of $y$. My attempt: $y^2 + (3x+1)\times y - 10x^2 + 5x = 0$ $\Rightarrow (y+(3x+1)/2)^2 - ((3x+1)/2)^2 = (x - (\frac 12)\times x)^2 - (\frac 12)^2 …
user262493
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how do you solve $(x^2-5x+5)^{x^2-36} =1$

Can someone please show me how they would work it out as I have never come across this before. $$(x^2-5x+5)^{x^2-36} =1$$
123pritch
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