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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If $a,b,c$ are three distinct positive real numbers then the number of real roots of $ax^2+2b|x|-c=0$ are

The equation can have two forms $$ax^2+2bx-c+0$$ Or $$ax^2-2bx-c=0$$ both discriminants of the equation are $${4b^2+4ac}$$ which is a positive value so roots are real. Then there should be four roots of the given equation, but answer says there are…
Aditya
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Finding the value of $p$ given the roots of a quadratic equation

Could you tell me how could I solve the value of $p$ in this question? For which $p$ does $3x^2+(p+1)x+24=0$ have one root equal to twice the other root? Options given are $\{\pm17,\pm19\}$ with all possible sign combinations.
Autumn Fall
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$(x-4)^2+8|x-4|+15=0$

The sum of the roots of the equation $(x-4)^2+8|x-4|+15=0$ is My attempt: Let $|x-4|=y$. So, the equation becomes $y^2+8y+15=0$. So, $y=-3,-5$. Both values should be rejected as $|x-4|$ cannot be negative. But the answer has been given as $16$.
aarbee
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How to show $\frac{300}{v} - \frac{300}{v+20} = 1.25$

A man travels a distance of $300$ km. On his return journey his average speed increased by $20$ km/h and his journey time decreased by $1\frac{1}{4}$ hours. If $v$ is the average speed of his outward journey how can we show that: $$\frac{300}{v} -…
imulsion
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find all values of y such that $(y^2+y-6)(x^2-6y+9)-2(y^2-9) = 0$

One of the questions on my Algebra 1 homework was to find all values of $y$ such that $$(y^2+y-6)(x^2-6y+9)-2(y^2-9) = 0$$ This was listed under "Lecture 13: Quadratic Equations" I can not figure out how to approach this problem? Should I expand it?…
Jamlandia
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How do you solve $\frac{x-1}{\sqrt{x}+2}=\frac{5}{2}$?

I solved it using the quadratic formula and it went like: \begin{gather} \frac{x-1}{\sqrt{x}+2}=\frac{5}{2} \\ 2(x-1)=5(\sqrt{x}+2) \\ 2x-2=5\sqrt{x}+10 \\ 2x-12=5\sqrt{x} \\ 4x^2+144-48x=25x \tag*{(squaring both…
Hubert Hanc
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If $\frac{x^2-bx}{ax-c} = \frac{k-1}{k+1}$ has roots, whose magnitude is equal but signs are opposite.

If $\frac{x^2-bx}{ax-c} = \frac{k-1}{k+1}$ has roots, whose magnitude is equal but signs are opposite. Answer is $\frac{a-b}{a+b}$ I used cross multiplication and since the roots are opposite in sign, on adding the roots, the total must be zero.…
sawan kumawat
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Alpha-beta quadratic equation

Question: The equation $$3x^2-6x-4=0$$ has roots α and β. Find the value of 1/α + 1/β. I'd just like confirmation on my answer, as I've already found the answer but am not confident in it. since αβ=c/a and α+β= -b/a 1/α +1/β= (α+β)/αβ=…
injustice fellow
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How to solve the quadratic equation with 2 unknown parameters for P as a function of w?

I tried to solve the following equations: $$-w^2 + 11w -11/2 = 10(w-P)-(w-P)^2$$ First, I got rid of the brackets and ended up with the following equation: $$w-11/2 = 2wP-10P-P^2$$ And now I am stuck. How do I solve this equation for P as a function…
Pam
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Calculating required length of conduit

We have a project at work where we are required to lay out network cable to multiple points along a number of benches, connected in a row. I have determined that any length of conduit is large enough to hold enough cable to supply 4 benches. If we…
Shane
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What causes the extraneous root when intersecting parabola $y^2=4ax$ with circle $x^2+y^2=9a^2/4$?

If I solve the parabola: $y^2=4ax$ and the circle: $x^2+y^2=\frac{9a^2}{4}$ I get a quadratic in $x$; ie: $$4x^2+16ax-9a^2=0$$ which has roots $x=\frac{a}{2},-\frac{9a}{2}$. But if we see the graphs of these two, both the intersections occur at…
Sanom Dane
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Integer Solutions for a Multivariable Quadratic

I'm solving a math puzzle and arrived at a quadratic:$$ \frac{6000n}{x(x-n)}=c $$ I only just graduated from high school and have very limited knowledge. I'm wondering if it's possible to find all integer solutions to this equation where $n$ and $c$…
Ethan Colgan
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Numbers of roots in Quadratic Equations

If $a,b,c,d$ are real numbers, then show that the equation $$(x^2 +ax -3b)(x^2-cx+b)(x^2 -dx +2b)=0$$ has at least two real roots.
user587196
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jenny farm and the dozen egg ???

Farmer Jenny decides to expand her business interests and starts to package and sell the eggs produced by her chooks to a local shop. The cost of producing $x$ dozen eggs per day is given by, in dirhams: $$C=( 5/12 x^2+ 4x-3)$$ and the selling…
moamen
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Solve one side of irregular quadrilateral with known area (formula help)

My question is about determining the formula for a missing length of a known area irregular quadrilateral. Its a fairly easy one, but i'm about 40 years outside of my math lessons! It's a land area problem - and I know the area, but don't know the…
Jason
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