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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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$x^{\frac{1}{2}}-3x^{\frac{1}{4}}-10=0$

$$x^{\frac{1}{2}}-3x^{\frac{1}{4}}-10=0$$ $$t=x^{\frac{1}{4}}$$ $$t^2-3t-10=0$$ $$\Delta=49$$ $$t_1=5$$ $$t_2=-2$$ And now I'm not sure what should I do... $$x_1^{\frac{1}{4}}=5$$ $$x_1=5^4=625$$ I'm not sure why did it work, but that's correct the…
nyasu
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Quadratic equation with indicies as another quadratic.

I'm trying to solve the following question below (Please do excuse the formatting)... $$x^{x^2-7x+11} = 1$$ Now, so far, I have calculated that as $1 =x^0$ that I can form an equation which is $$x^2 - 7x+11 = 0$$ and the values of x that it gives…
vik1245
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The quadratic equation $x^2 + Lx + M = 0$

The question: The quadratic equation $ x^2 + Lx + M = 0$ has one root twice the other. a) Prove that the roots are rational whenever L is rational. I was able to find out that due to one root being twice the other that $2L^2 = 9M$ and the…
006609
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Inequation with 2 variables - how to proceed?

Find the highest value of $K$ such that $$x^2 - 10x + 40 \ge K$$ $ \forall x \in R$. Step 1: I'll assume $K$ is equal to $0$ just to make it simpler (Is it OK to do so?) $$x^2 - 10x + 40 \ge 0$$ Step 2: Solving this with the quadratic…
ogondiaz
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How should I proceed with this inequation?

$$(2x + 1)(3x - 5) - 4x(x-3) + 7 \leq 0$$ (is less or equal than "0", someone help me to edit that part). Step 1: $$6x^2 - 10x + 3x - 5 - 4x^2 + 12x + 7 \leq 0$$ Step 2: $$2x^2 - 19x + 7 \leq 0$$ Step 3: $$ x = \frac{19 + \sqrt{-(19)^2 -…
ogondiaz
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Solving an equation containing 4th power of variable.

I know how to solve Quadratic equations. Recently i came across the equation of type $ax^4 + bx^2 + c = 0$ and i had to solve it. So what i did is that i supposed $x^2 = y$ so that the above equation becomes: $ay^2 + by + c = 0$ and i found y by…
user258250
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Find the values of a, b and c

The question: Find values of $a,b,c.$ if $\displaystyle \frac{x^2+1}{x^2+3x+2} = \frac{a}{x+2}+\frac{bx+c}{x+1}$ My working so far: http://i.imgur.com/VegifVa.jpg How do I isolate $a$, $b$ and $c$?
Jaskirat Boparai
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Better way of solving this quadratic equation?

This is the excersice: $$x^2 - 2mx - 2m - 1 = 0$$ I've done this: 1.- $$x^2 - (2mx -2m) - 1 = 0$$ 2.- $$x^2 - (2m(x-1)) - 1 = 0$$ I think I need to transform: $$(2m(x-1))$$ to something of the form $$mx$$ And then to have something like: $$x^2 -…
Valeria Gonzales
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quadratic equation with zero product

I have this equation ${3x^2 -12 = -9}$ The answer the text book gives is ${x = 1}$ or ${x = 3}$. But I would solve it by first of all dividing 3 on both sides which gives: ${x^2 -4 = -3}$ Then add +3 to both sides which gives: ${x^2 -1}$ Which gives…
dagda1
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how to solve the question with one unknown variable?

This is the Question: 5 years ago, Ebo was 3 times as Old as Atu.In 3 years, Ebo will be twice as old as Atu. What is the sum of their ages now? I am easily able to solve it with two unknown variables. How can I solve this question with one unknown…
user2401175
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quadratic equation with imaginary part

How can we solve this equation $x^2-bx-c=0$ where c is not real number. I tried to solve the above equation but I am not sure if it is correct or not. $x_{1,2}=\frac{b}{2}\pm \frac{\sqrt{b^2+4c}}{2}$ I do not know what is the next step to solve…
David
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Two quadratic equations to get an expression

If $a (p+q)^2+2apq+c=0 $ and $a (p+r)^2+2apr+c=0 $ then find $ q.r $ in terms of $ p, a, c$ My try: I tried to equate both equations and got the relations that either $ a=0, q=r, q+r+4p=0 $ Then I tried to square $q+r+4p=0 $ and got $ q.r=16\frac…
Kartik Watwani
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Nature of Roots of quadratic $af(x) = (x^2+2)(a-1)$

I need help with the following. The problem is stated like so: "The value of the constant $a$ is such that the quadratic function $f(x) \equiv x^2 +4x + a +3$ is never negative. Determine the nature of the roots of the equation $af(x) =…
Naz
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Ranges of k values in quadratic for it to be positive

Here is the problem $2x^2+6x+1+k(x^2+2)$, find the condition that must be satisfied by k in order that the expression may be positive for all real values of x. The quadratic of the form $ax^2+bx+c$ will be positive for all real values of x, if…
Naz
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How do I find a variable when there is a polynomial?

So I have two similar questions: $x=x_0 + v_0t + \frac{1}{2}at^2$ where I have to solve for $t$ and $mgx + \frac{1}{2}kx^2 = \frac{1}{2}mv^2$ where I have to solve for $x$ I'm not sure if I have to use the quadratic equation or what.
TakamaruTaihou
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