To solve the problem, we need to find the value of the expression (1+α+α2)(1+β+β2), where α and β are the roots of the quadratic equation ax2+bx+c=0. 1. Identify the roots: Given the quadratic equation ax2+bx+c=0, we know that: - The sum of the roots α+β=...
If α and betaarethes√ofax^2+bx+c=0andalpha+beta,alpha^2+beta^2,alpha^3+beta^3are∈GP(GeometicProgression)andDwlta-b^2-4acthen AΔ≠0 BbΔ=0 CcΔ=0 DΔ=0Submit Question 3 - Select One If α,β are the roots of ax2+bx+c=0, then αβ2+α2β+αβ is equal to Ac...
Q. If α1,α2,α3,α4 be the roots of x5−1=0 then find ω−α1ω2−α1⋅ω−α2ω2−α2⋅ω−α3ω2−α3⋅ω−α4ω2−α4 Q. If 1a+ω+1b+ω+1c+ω+1d+ω=2ω, where a,b,c are real and ω is a non-real cube root of unity, ...
If A and B are Hermitian operators, prove that <A2>⩾0. Hermitian Operator: An adjoint of itself is a Hermitian operator. The Hermitian operator produces actual eigenvalues when applied to a quantum state. The eigenvalues are known as energy eigenvalues when the Hamilto...
What is the x component of r = a - b + c, if a = 3.5 + 8.4 - 4.2, b = -1.8 + 1.5 + 7.7, and c = 6.1 + 4.4 + 2.4? Equation: A mathematical statement that describes the relationships among the variables and constant value ...
(击鼓) styles on tree roots.Researchers observed their drumming styles range from rock to jazz.One chimpanzee brought back the style of the late John Bonham,a drummer who played a piece of music,Whole Lotta Love,and is ranked as one of the best."The chimpanzee makes very ...
Since , αandβ are the roots of the equation ax2+bx+c=0, then, Sum of the roots , α+β=−ba and Product of the roots, αβ=ca The expression, (aα+b)−1+(aβ+b)−1 1aα+b+1aβ+b=αβ+b+aα+b(aα+b)(aβ+b) a(α+β)+2ba2αβ+ab(α+β)+b2...
If alpha and beta are the roots of x^2 +px + q=0 and alpha^4, beta^4 are the roots of x^2-rx +s=0, then the equation x^2 -4qx+ 2q^2 -r=0 has always
Let a, b, c be real, if ax2+bx+c=0 has two real roots α,β, where a<−1andβ>1, then the value of 1+ca+∣∣∣ba∣∣∣ is : A a. less than -1 B b. greater than zero C c. equal to zero D d. equal to b2−4ac Video SolutionText...
To solve the problem, we need to find the value of α2009+β2009 where α and β are the roots of the equation x2−x+1=0. Step 1: Find the roots α and β The roots of the quadratic equation ax2+bx+c=0 can be found using the quadratic formula: x=−b±√b2−4ac2a For...