Mathematics Stack Exchange
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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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question on quadratic expansion

I have been trying to solve this question, but no luck so far, any help would be appreciated. Let $a,b,c > 0$ be such that $a^2 + b^2 -2bc =100, \ 2ab -c^2 = 100$. Then the value of $\dfrac{a+b}{c}$ is: ... (the options are $10$, $100$, $2$, $20$)
Pharaoh
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quadratic equation form maximum solutions

My Pearson intermediate algebra book has a "concept check" question in its section on solving equations by using quadratic methods. These questions are supposed to highlight fundamental concepts that indicate full or poor understanding of the…
saucyplankton
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Weird property of quadratic equations

Today, we learnt about the quadratic formula, and I noticed a strange property of (seemingly) all quadratic equations. If we call the two solutions of any arbitrary quadratic equation $x_1$ and $x_2$: $$When \ a=1: b=-(x_1+x_2)$$ Why is this? I've…
Nico A
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Indices and Bases: Solve "x"

Solve the equation $2^x - 3^{x-1}=-(x+2)^2$ How I got this question? I created this question so I know the answer. The answer is 5. But I have no idea how to solve it. Take note that I cannot do logarithm, guess and check and modulus. Does anybody…
ministic2001
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Writing an equation from data

Wendy, Elizabeth, and Charlie are all working on a math problem together and they are having a disagreement.: Ticket lines are huge at the Math Olympics ticket office. Pi, the local math team, is competing to be the Math Champions. When tickets…
Dana
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Why not always use the quadratic equation

The is a very simple question, but I have just started studying quadratics. I understand how to factor them using different methods and also understand solving a quadratic using the formula, but my question is why bother learning to factorise when…
user2145312
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How do I factorise this difficult quadratic without a calculator?

On one of the UKMT maths challenge past papers(Team challenge) it asks you this question: Factorise $120x^2 + 97x - 84$ That is the whole question. I used a calculator and found that you factorise it into $(40x-21)(3x+4)$ Bearing in mind that a…
Augs
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How to solve the following quadratic word problem?

The total cost of carpeting a rectangular room is given the expression $$6x^2 + 18x$$ This is the multiple choice type question so the given options were set up like this. The length of the room is_______feet, its width is ____ feet and the cost of…
MATH ASKER
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If $m,M$ are the minimum and maximum value of $\alpha^2+\beta^2$,then find $m+M.$

Let $\alpha,\beta$ be real roots of the quadratic equation $x^2-kx+k^2+k-5=0$.If $m,M$ are the minimum and maximum value of $\alpha^2+\beta^2$,then find $m+M.$ I calculated…
Vinod Kumar Punia
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Sum of all values of $b$ if the difference between the largest and smallest values of the function $f(x)=x^2-2bx+1$ in the segment $[0,1]$ is $4$

Find sum of all possible values of the parameter $b$ if the difference between the largest and smallest values of the function $f(x)=x^2-2bx+1$ in the segment $[0,1]$ is $4$. I found that the smallest value of $f(x)=x^2-2bx+1$ is $1-b^2$ But i do…
Vinod Kumar Punia
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If $a,b$ are the roots of the equation $x^2-2x+3=0$ obtain the equation whose roots are $a^3-3a^2+5a-2$, $b^3-b^2+b+5$

I have been trying this using sum of roots and product of roots but it gets too lengthy. So I found the roots of the given equation which are imaginary and tried to replace the values in the two given roots. Still I am not able to solve this.
user295884
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Finding the values of $5a+b$ if $ax^2+bx+10$ does not have $2$ distinct roots

If $ax^2+bx+10=0$ does not have two distinct real roots where( $a$ and $b$ are real) then the possible values of $5a+b$ from the given 4 options(as obviously there can be infinite possible values..but I only need to find out which of the four given…
Freelancer
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Do i need to always take out factor of -1 when solving a quadratic in form $ax^2 + bx + c$ when $a$ is negative?

In my textbook I am advised to always take out the factor of -1 if the quadratic is in the form of $ax^2 + bx + c$ when $a$ is negative. For example: $-4x^2 + 4x + 3$ My question is, is this compulsory or could it be resolved without taking out…
Pawel
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Interval in which roots lie given inequality between coefficients

Given that in a quadratic equation $ax^2+ bx + c=0$, $(4a+c)^2<4b^2$, Find the interval in which roots lie. I subtracted $16ac$ from both sides, to get $\Delta>(4a-c)^2$, which is always greater than zero, hence roots are real. but otherwise, I…
GRrocks
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Quadratic formula does not work

If I put the equation: $5x^2-x-4 =0$ in the quadratic formula, than I get $x = 1$ or $x = \frac{-4}{5}$ but the real zeros are: $x = -1$ or $x = \frac{4}{5}$ Can somebody explain me if the quadratic formula fails or me?
wajnoem
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