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
1
vote
3 answers

Completing the square help

The textbook gives this equation: ${12x^2 + 24x -8x = 0}$ with an answer of ${x = 0}$ or ${x = -{4\over3}}$ But I suspect it should be ${12x^2 + 24x -8 = 0}$ So in order to solve this, I would first isolate the x terms on one side of the equation by…
dagda1
  • 825
1
vote
1 answer

Solving a exponential quadratic equation

Find t given: $$0.715+258.115e^{-0.5t}-67.83e^{-0.25t}=0$$ Please help. I've substituted $e^{-0.5t}$ for $x$ and did $$-67.83x^2+258.115x+0.715=0$$ but the answer is not coming out? Am I doing something wrong because it doesn't follow the quadratic…
Grace
  • 23
1
vote
3 answers

Simultaneous equations, $\frac{1}{x}+\frac{1}{y}=1$,$x+y=a$,$\frac{y}{x}=m$

By eliminating $x$ and $y$ from the following equations, I need to find the relation between $m$ and $a$. \begin{align*} \frac{1}{x}+\frac{1}{y}=1 \\ x+y=a \\ \frac{y}{x}=m \end{align*} I tried different ways, but cannot arrive at the answer. I end…
Naz
  • 3,289
1
vote
2 answers

This is equation is giving me issues $x^2 - 6x + 15 = 0 $

I was given this equation $x^2 - 6x + 15 = 0 $ I tried to look for numbers whose sum is big and product of ac and i could not find any. I tried using the quadratic formula $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ and this is what i got $x =…
user249954
1
vote
2 answers

Question on proving quadratic inequality

Let $ax^2+bx+c$ = 0 be a quadratic equation and $\alpha$,$\beta$ are real roots. Condition for $\alpha < -1$ and $\beta > 1$. Show that $1 +\frac{c}{a}$ + $\left|\frac{b}{a}\right| < 0$. I have tried but could not prove this inequality. I want…
satyatech
  • 517
1
vote
2 answers

Solve x for a quadratic equation (not finding zeroes)

With a linear function $f(x)=5x+2=q$ can be solved for $x$ by rewriting it as $x=(q-2)/5$ While with a quadratic function $f(x)=5x^2+2x+2=q$ how would you solve for both x's on one side? So you clearly can not add the solutions for $5x^2=q$ and…
Euler77
  • 63
1
vote
1 answer

solving the equation by reducing it to quadratic form

Solve for $x$ $$4^x-\dfrac{3^x}{\sqrt3}=3^x\cdot\sqrt3-\dfrac{2^{2x}}2$$ I don't understand how to convert it into quadratic equation how should I equate all bases
tapadia newlon
  • 77
1
vote
2 answers

Quadratic question problem

I have been asked to look at a yr 12 question about a space ships trajectory modelled by a quadratic equation. But my solution to the question has a negative minimum for distance at a time of T = 13 minutes. I was wondering if anyone can confirm…
Michael T Mckeon
  • 451
1
vote
3 answers

Nature of roots of a quadratic equation with irrational co-efficients

What would be the nature of the roots of the equation $$2x^2 - 2\sqrt{6} x + 3 = 0$$ My book says that as the discriminant is 0 so the roots are rational and equal. But discriminant can be used for determining the nature of roots only when the roots…
user456
  • 709
1
vote
1 answer

IIA problem on Quadratic Equations.

How to show that expression $$\frac{px^{2}+3x-4}{p+3x-4x^2}$$ will be capable of all values when $x$ is real,provided that $p$ has any value between $1$ and $7$? Regarding my personal attempts,they are all futile. I tried to…
user237454
1
vote
3 answers

How do I find the value of n in the following equation

This is from the controversial GCSE question in the UKs recent exams. The orginal question is thus: There are $n$ sweets in a bag. $6$ of the sweets are orange, the rest are yellow. Hannah takes at random a sweet from the bag and eats it. She then…
MrDobilina
  • 113
1
vote
4 answers

What two numbers when multiplied gives $-25$ and when added, $-10$?

Factors of $25$ are; $1, 5, 25$ $$5 \times 5 = 25$$ $$5 + 5 = 10$$ $$-5 \times 5 = -25$$ $$-5 + 5 = 0$$ How can I solve this? Thanks
user214824
1
vote
2 answers

To find $x$ in $x^2 -8x-11=0$

$x^2 -8x-11=0$ I have tried factorising but it won't factorise into a quadratic equation Hi, It would be great if you could complete this question with working and post it. Thx The two solutions of $x^2 -8x -11=0$ are in the form $x=p +\- Q root 3$…
Jason
  • 21
1
vote
0 answers

Having trouble with finding a Quadratic Expression

I am having trouble trying to work out a quadratic expression for uni, being a external student its hard to find help. My problem is Perimeter = 1000m Part 1 Solve L in terms of w in regard to the perimeter I worked out $l = \frac{P - 2w}{2}$ Part…
Ashley Hughes
  • 121
1
vote
2 answers

For which $m$ does the equation $\lvert x^2+5x+4 \rvert +x-m=0$ have more than two real solutions?

When dealing with problems containing quadratic equations, I've never come across one that deals with a number of roots that is bigger than 2. I've tried breaking up the function into two parts. $x^2+6x+4-m=0$ for…
John Doe
  • 1,080
1 2 3
…
64 65