Let α and ß be the roots of equation x^2-6x-2=0. If a_n=α^n-ß^n, for n≥1, then the value

Let α and ß be the roots of equation x^2-6x-2=0. If a_n=α^n-ß^n, for n≥1, then the value of (a_10-2a_8)/(2a_9 ) is equal to: (a) 3 (b) -3 (c) 6 (d) -6 quadratic equation, Impetus gurukul #quadratic_equation @Impetus Gurukul -- To buy complete Course please Visit– https://www.impetusgurukul.com or contact on 7047832474 join Impetus Gurukul live classes via the official Website: https://live.impetusgurukul.com -- Algebra Playlist: Permutations & Combinations:    • Permutations & Combinations   Matrices:    • Matrices   Determinants:    • Determinants   Binomial Theorem:    • Binomial Theorem   Progression ( A.P,G.P, H.P & Special Series):    • Progression ( A.P, G.P, H.P & Special Series)   Quadratic equation & Inequations:    • Quadratic equation & Inequations   Set & Relations:    • Set & Relations   Complex Number:    • Complex Number   -- Our Social links Telegram: https://t.me/impetusgurukul Facebook:   / impetusgurukul   LinkedIn:   / dr-sharad.  . twitter:   / impetussharad   --- Quadratic Equations A quadratic equation in the variable x is an equation of the form ax2 + bx + c = 0, where a, b, c are real numbers, a 0. In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. But when we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation. That is, ax2 + bx + c = 0, a 0 is called the standard form of a quadratic equation. In general, a real number is called a root of the quadratic equation ax2 + bx + c = 0, a 0 if a 2 + b+ c = 0. We also say that x = is a solution of the quadratic equation, or that satisfies the quadratic equation. Note that the zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same. Quadratic Formula = [-b ± √(b² - 4ac)]/2a Important Quadratic Equation Formulas The following list of important formulas is helpful to solve quadratic equations. • The standard form of a quadratic equation is ax2 + bx + c = 0 • The discriminant of the quadratic equation is D = b2 - 4ac • For D ‘Greater than’ 0 the roots are real and distinct. • For D = 0 the roots are real and equal. • For D ‘Less than’ 0 the roots do not exist, or the roots are imaginary. • The formula to find the roots of the quadratic equation is x = −b±√b2−4ac2a−b±b2−4ac2a. • The sum of the roots of a quadratic equation is α + β = -b/a = - Coefficient of x/ Coefficient of x2. • The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x2 • The quadratic equation having roots α, β, is x2 - (α + β)x + αβ = 0. • The condition for the quadratic equations a1x2+b1x+c1=0a1x2+b1x+c1=0, and a2x2+b2x+c2=0a2x2+b2x+c2=0 having the same roots is (a1b2−a2b1)(b1c2−b2c1)(a1b2−a2b1)(b1c2−b2c1) = (a2c1−a1c2)2(a2c1−a1c2)2. • For positive values of a (a ‘Greater than’ 0), the quadratic expression f(x) = ax2 + bx + c has a minimum value at x = -b/2a. • For negative value of a (a ‘Less than’ 0), the quadratic expression f(x) = ax2 + bx + c has a maximum value at x = -b/2a. • For a ‘Greater than’ 0, the range of the quadratic equation ax2 + bx + c = 0 is [b2 - 4ac/4a, ∞) • For a ‘Less than’ 0, the range of the quadratic equation ax2 + bx + c = 0 is : (∞, -(b2 - 4ac)/4a] --- +quadratic equation,Impetus gurukul,Relationship Between Coefficients and Roots of Quadratic Equation,Quadratic Equation solutions,JEE previous year's question's solution,Quadratic Equation - Formulas,Tricks for Solving Quadratic equation,solve quadratic equation,Quadratic equation roots formula,Sum and product of roots of quadratic equation