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
3
votes
3 answers

Finding zeroes of a polynomial with parameter

Problem description says that for the function: $$ f(x) = mx^2 + x + m - 1 $$ There are two different zeroes out of which both are lesser than 1. I'm tasked with finding all values of m that would fulfill this requirement. First step was to see…
Marek M.
  • 279
3
votes
2 answers

Trying to solve this simple equation

I have something like this: If $A > B$, then $X = A - B$, else $X = B - A$. $X$ and $B$ are known to me, but $A$ is not known to me. Now I have $C$ (which is to basically replace $B$ in the above conditional equation). I want to get $Y$, If $A >…
kishoredbn
  • 311
3
votes
1 answer

Question on quadratic problem set

Okay so I have a quadratic function problem. I will omit the problem for now just because we don't really need it. My problem is: M is surface area. Do I have to write M(x, y) or just M in the area I've bolded? Here is my work: Problem 2 x =…
Someone
  • 167
  • 5
3
votes
2 answers

Question under quadratic equation

Let $f(x)=x^2 + ax + b$ such that $f(2)\times f(3)= \frac{1}{2}$ and $1< f(2) + f(3)< 2$, then the equation $f(x)=1$ has $(a,b \in \mathbb{R})$ Both roots real and distinct Both roots real and equal Non real roots Roots whose nature depends on…
Prajwal Turkar
  • 57
3
votes
9 answers

How to tackle this squaring of inequality problem

If the roots of quadratic equation $$x^2 − 2ax + a^2 + a – 3 = 0$$ are real and less than $3$, find the range of $a$. The roots are $a \pm \sqrt {3 – a}$ For the roots to be real, we must have a < 3. Also, for the roots to be less than…
Mick
  • 17,141
3
votes
2 answers

Number of real solutions of the equation $6x^2 -77[x] + 147 =0 $.

How many real solutions of $$6x^2 -77[x] +147=0$$ are there, where $[x]$ is the integral part of $x$? The answer says 4 solutions but I got none. As: $6x^2 + 147 = 77[x]$ LHS= integer Therefore, RHS = integer Then $6x^2$ just be integer Then …
Hritwik Raj
  • 71
  • 5
3
votes
3 answers

quadratic equation

If $\alpha$ is root of equation $x^2+x+1 = 0$ then find the value of $1+\alpha +\alpha^2+\alpha^3+\cdots+\alpha^{2010}$ Here I have put the value of $\alpha$ in the given equation to get $1+\alpha + \alpha^2$ which is similar to the first three…
Sachin Sharmaa
  • 621
3
votes
1 answer

Quadratic Equation using surds property

$$\left(\sqrt{2+\sqrt{3}}\right)^x+\left(\sqrt{2-\sqrt{3}}\right)^x=2^x$$ Using property of surd can we simplify the above expression like: $$\left(\frac{\sqrt{3}+1}{\sqrt{2}}\right)^x +\left(\frac{\sqrt{3}-1}{\sqrt{2}}\right)^x=2^x$$ Am I right…
Sachin Sharmaa
  • 621
3
votes
2 answers

What do the $p$ and $q$ stand for in this quadratic formula?

I study Computer Science in a German university and they use another formula to solve the quadratic equations. They call it the P-Q-Formel. I'm used to this formula. While the Germans use this one. Normally I'd find the values of a, b , c and D and…
Ariel H.
  • 31
  • 7
3
votes
2 answers

Solve : $x^6 - 12x^5 + ax^4 + bx^3 + cx^2 + dx + 64 =0$ has all positive roots then the values of $a , b , c$ and $d$ are

My try : Tried to solve by relation between coefficient and roots of n- degree equations but unable to proceed because of the variables. But just found the interesting thing that the signs of $a , b , c$ and $d$ are as same as in relation. Answer :…
Shinobi
  • 351
  • 4
  • 14
3
votes
2 answers

Finding value of Quadratic

If the quadratic equations $3x^2+ax+1=0$ and $2x^2+bx+1=0$ have a common root, then the value of $5ab-2a^2-3b^2$ has to be find. I tried by eliminating the terms but ended with $(2a-b)x=1$. Can you please suggest how to proceed further?
user532267
  • 41
3
votes
1 answer

If $ax^2+bx+c=0$ has $2$ different solutions in $(0,1)$ then prove $a\geq 5$.

Say $a,b,c$ are integers, $a>0$. Suppose $ax^2+bx+c=0$ has $2$ different solutions in $(0,1)$ then prove $a\geq 5$. Find an example for $a=5$. I am struggling with this for some time with no success. I try Vieta's formula $0
nonuser
  • 90,026
3
votes
6 answers

Condition for $ax^2 + bx + c > 0$ or $ax^2 + bx + c < 0$

In an inequality question I was solving, I got to a step where I was stuck. $$\frac{(x-1)(3x-8)}{x^2-3x+4} \ge0$$ I couldn't solve it because I cannot factor the denominator or predict its sign. The solution manual says that, $x^2-3x+4>0$ because…
Raknos13
  • 572
3
votes
2 answers

Find Value of A if there is one real solution

For what value of a will this equation have only one real root: $$(2a−5)x^2−2(a−1)x+3=0$$ Note: $x$ is a variable If found that $a=4$ works, but there seems to be another solution. Any help?
Daniel Lobo
  • 31
3
votes
1 answer

Number of ordered pairs to have integral roots

The question is to find out the number of ordered pairs $(a,b)$ where $a,b$ are non negative integers such that the equations $x^2-2ax+b=0$ and $x^2-2bx+a=0$ have integral roots. For the roots to be integers the discriminant must be a perfect…
user471651
  • 1,164
1 2 3
…
64 65