I tried finding the common difference between the roots but didnt know what to do next.
if someone could tell me how to solve this or give a headstart itll be a lot helpful
2026-03-25 07:48:25.1774424905
Roots of quadratic eqaution lies in an AP
27 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ROOTS
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Roots of a complex equation
- Do Irrational Conjugates always come in pairs?
- For $f \in \mathbb{Z}[x]$ , $\deg(\gcd_{\mathbb{Z}_q}(f, x^p - 1)) \geq \deg(\gcd_{\mathbb{Q}}(f, x^p - 1))$
- The Heegner Polynomials
- Roots of a polynomial : finding the sum of the squares of the product of two roots
- Looking for references about a graphical representation of the set of roots of polynomials depending on a parameter
- Approximating the first +ve root of $\tan(\lambda)= \frac{a\lambda+b}{\lambda^2-ab}$, $\lambda\in(0,\pi/2)$
- Find suitable scaling exponent for characteristic polynomial and its largest root
- Form an equation whose roots are $(a-b)^2,(b-c)^2,(c-a)^2.$
Related Questions in QUADRATICS
- Do you have to complete the square before using the quadratic formula?
- Roots of the quadratic eqn
- Questions on positivity of quadratic form with orthogonal constraints
- Conjugate quadratic equations
- Do Irrational Conjugates always come in pairs?
- Quadratic Equations and their roots.
- Solving a quadratic equation with square root constants.
- What would the roots be for this quadratic equation $f(x)=2x^2-6x-8$?
- Polynomial Equation Problem with Complex Roots
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
Related Questions in ARITHMETIC-PROGRESSIONS
- How to solve a quartic equation given that the roots are all part of an arithmetic sequence?
- Defining a rigorous equation for the distance
- How do I solve the following exercise?
- Upper bound for recursion?
- $a, 1, b$ are three consecutive terms of an arithmetic series, find $a, b$ and $S$ of the infinite geometric series
- I am stuck on a question Algebra:Sequence and series, Can we make an infinitely long arithmetic progression from the set of prime integers?
- General formula for natural power summation
- How do I proceed with this?
- Find the total number of identical terms in 2 sequences.
- Is there generalization for gamma function?
Related Questions in DISCRIMINANT
- discriminant and irreducibility of $x^p - (p+1)x - 1$
- Discriminant of $X^n+pX+q$
- How to solve $ax^x+bx+c=0$?
- galois group of irreducible monic cubic polynomial
- discriminant as a product of pairwise differences of roots
- Irreducibility of $x^3-6x-2$ in $Q[x]$
- Find the points that are closest and farthest from $(0,0)$ on the curve $3x^2-2xy+2y^2=5$
- Find k for Positive Definite Quadratic Form
- Minimize objective function for least square classification
- Quadratic Equations(determine the nature of roots)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
HINT
The formulae for sum and product of roots gives $\frac{b^2-4ac}{a^2}=(\alpha - \beta)^2$. Compare this with the same result for the other quadratic and note that $\alpha-\beta=\gamma-\delta$.
NOTE
$(\alpha - \beta)^2=(\alpha + \beta)^2-4\alpha\beta =\frac{b^2}{a^2}-4\frac{ac}{a^2}$