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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Using the complete the sqaure formula.. $2x^2 - 4x +1 = 0$

So Im using the complete square method and i was just wondering where am i going wrong. I'm solving this $2x^2 - 4x +1 = 0$ So i am using this rules. $$ax^2 + bx +c = 0$$ subract c from both sides; $ax^2 + bx = -c$ divide by a $ x^2 +…
user243383
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Finding chord length with Sum and products?

The line $x + y − 1 = 0$ intersects the circle $x^2 + y^2 = 13$ at $A(\alpha_1, \alpha_2)$ and $B(\beta_1, \beta_2)$. Without finding the coordinates of A and B, find the length of the chord AB. Hint: Form a quadratic equation in $x$ and evaluate…
user255479
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I am not getting roots of $x^4-4x^3+3x^2+2x-30=0$

Applying Descartes's method, I determined the interim equation as $y^4-3y^2-28=0$. Then I went on to treat this as a product of $(y^2+ky+m)(y^2-ky+n)$. Comparing coefficients of $y^2$, $y$ and constant term, I obtained $m+n-k^2=-3$, $k(n-m)=0$ and…
Mahesha Pandit
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Question on Quadratic equation

Q- If roots of quad. Equation $x^2-2ax+a^2+a-3=0$ are real and less than $3$ then, a) $a<2$ b)$24$ In this ques., i used $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ and then if $a$ will be $1,2$ only then the root will be defined but if we use $3$…
Kuljeet
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Solving a quadratic equation with complex coefficient

Express $z4$=-$\sqrt{3}$+i in polar form. Hence solve the equation $Z^2$=$z4$ for $z$ a complex number. You may leave the answer in polar form. My answer: $z4$ in polar form is 2cis-30$^{\circ}$ and thats as far as I have gotten. I have seen this…
jon
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values for which quadratic curve lies below x axis

A quadratic equation $y=(k+1)x^2-3x+(k+1)$ we need to the find the set of values of $k$ for which the curve $y$ lies below the $x-$ axis. I used the quadratic formula and equate it to $0$ $ 3\pm \frac{\sqrt{ 9-4(k+1)^2}}{2(k+1)}=0 $ PS assist, how…
Arif
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If a line parallel to $y=-7x+3$ touches the parabola $2x^2-3x+2$ in the point $(x_0,y_0)$, what is the value of $4x_0+y_0$?

I tried solving this but I've no idea how to find the point where a line of the form $y=-7x+n$ intersects a given parabola. Hints are welcome. Don't know calculus (don't even know if it's applicable here, but either way).
John Doe
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I have no idea what below surface equation represent

I have the equation: $$x^2+y^2+4z^2-14xy+8xz-8yz=24$$ What does this equation represent? How can I find the "axes" of it (?), and is it possible to draw it when it intersect the plane $z=0$?
monday25
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Real world example of need for quadratic equation

I am (re)learning the quadratic equation. Having a concrete understanding of its purpose would really help, but I can not find any examples of a real-world scenario that requires the use of it that are more specific than "it's used by engineers" or…
Choylton B. Higginbottom
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If a quadratic equation can have less then two solutions

is there anyway that a quadratic equation has less than two solutions? If the first coefficient a is 0, then it is not a quadratic.
tina mott
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Approaching this proof problem? If $0 \le x \le 3$ then $12 - 7x + x^2 \ge 0.$

Prove that if $x$ is a real number in the range $12 - 7x + x^2 \ge 0.$ Which type of proof should I use to solve this? At first I thought direct proof. Choosing a number between $0$ and $3$ and attempting to solve?
kvax12v
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Finding value of $m$ which is a part of a quadratic

Q : $$m \gt 2$$ $$x^2 + (m-3)x - 2 = 0$$ If $|x_1 - x_2| = 3$, so $m = ?$ Stuck here. Please give me a hint
Oğuz İsmayil uysal
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An equation with negative exponents in quadratic equations test

There is a problem like this : $x^{-1} = 2x^{(-1/2)} + 3 , x = $? in my test. I'm working on it for a half of hour but still i can't solve. Please help me. (Excuse my bad grammar)
Oğuz İsmayil uysal
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How to solve this quadratic equation?

So I've got this quadratic equation and am totally unable to solve it. Can someone tell me how to do it? $$\frac{a}{ax-1} + \frac{b}{bx-1} = a + b,$$ where $x$ is not equal to $\frac{1}{a}$ or $\frac{1}{b}$. We need to solve for $x$.
Bone
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