Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Quadratic Equation

Let α, β be roots of x^2+ 2 x-8=0 . If U_ n =α^ n +β^n , then U_ 10...

Let α,β\alpha, \beta be roots of x2+2x−8=0x^2+\sqrt{2} x-8=0. If Un=αn+βn\mathrm{U}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^n, then U10+2U92U8\frac{\mathrm{U}_{10}+\sqrt{2} \mathrm{U}_9}{2 \mathrm{U}_8} is equal to______

Correct answer

0

Step-by-step solution

α10+β10+2(α9+β9)2(α8+β8)α8(α2+2α)+β8(β2+2β)2(α8+β8)8α8+8β82(α8+β8)=4\begin{aligned} & \frac{\alpha^{10}+\beta^{10}+\sqrt{2}\left(\alpha^9+\beta^9\right)}{2\left(\alpha^8+\beta^8\right)} \\ & \frac{\alpha^8\left(\alpha^2+\sqrt{2} \alpha\right)+\beta^8\left(\beta^2+\sqrt{2} \beta\right)}{2\left(\alpha^8+\beta^8\right)} \\ & \frac{8 \alpha^8+8 \beta^8}{2\left(\alpha^8+\beta^8\right)}=4\end{aligned}
Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 +… JEE Advanced 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n ∈ ℝ .… JEE Main 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be… JEE Main 2026Let e_1 and e_2 be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets \ a… JEE Main 2026Let α, β be the roots of the equation x^2 - x + p = 0 and γ, δ be the roots the equation… JEE Main 2026Let a, b ∈ ℂ . Let α, β be the roots of the equation x^2 + ax + b = 0 . If β - α = 11 and… JEE Main 2026Let A, B , where A, B ∈ (-(π)/(2), (π)/(2)) , be the roots of the quadratic equation x^2… JEE Main 2026If α=1 and β=1+i 2 , where i= -1 are two roots of the equation x^3+ax^2+bx+c=0 , a,b,c ∈… JEE Main 2026If the quadratic equation (λ+2)x^2-3λ x+4λ=0 , λ ≠ -2 , has two positive roots, then the… JEE Main 2026Let α, β be the roots of the equation x^2 - 3x + r = 0 , and (α)/(2), 2β be the roots of… JEE Main 2026Let a, b, c ∈ \ 1, 2, 3, 4\ . If the probability, that ax^2 + 2 2 \,bx + c > 0 for all x… JEE Main 2026Let S=\ x^ 3 +a x^ 2 +b x+c: a, b, c ∈ ~N. and .a, b, c ≤ 20\ be a set of polynomials.… JEE Main 2026If α, β , where α<β , are the roots of the equation λ x^ 2 -(λ+3) x+3=0 such that… JEE Main 2026The smallest positive integral value of a , for which all the roots of x^ 4 -a x^ 2 +9=0… JEE Main 2026The sum of all the real solutions of the equation _ (x+3) (6 x^ 2 +28 x+30)=5-2 _ (6… JEE Main 2026 Full Quadratic Equation list Quadratic Equation JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs