TS EAMCET · Maths · Complex Number
If \(\alpha, \beta\) are the roots of the equation \(x^2-2 x+2=0\) then \(\alpha^{2020}+\beta^{2020}=\)
- A \(2^{1011}\)
- B \(-2^{1011}\)
- C \(2^{2021}\)
- D \(2^{-2021}\)
Answer & Solution
Correct Answer
(B) \(-2^{1011}\)
Step-by-step Solution
Detailed explanation
Given equation is \(x^2-2 x+2=0\) \[ \begin{aligned} & \therefore \alpha+\beta=2 \text { and } \alpha \cdot \beta=2 \\ & \because(\alpha-\beta)^2=(\alpha+\beta)^2-4 \alpha \beta=4-8=-4 \\ & \alpha-\beta= \pm 2 i \\ & \alpha+\beta=2 \end{aligned} \] On solving equations (i) and…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Match the following
0
TS EAMCET 2017 Medium - Let \(A B C D\) be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression. If the centroid \(G\) of the tetrahedron is \((2,3, k)\) then the distance of \(G\) from the origin isTS EAMCET 2020 Medium
- If \(\cos ^{-1}\left(\frac{1}{2}\right)=\cot \left(\cos ^{-1} x\right)\), then the value of \(x\) isTS EAMCET 2015 Easy
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-\mathrm{Px}^2+\mathrm{Q} x-\mathrm{R}=0\) and \((\alpha-2)^2,(\beta-2)^2\), \((\gamma-2)^2\) are the roots of the equation \(x^3-5 x^2+4 x=0\), then the possible least value of \(\mathrm{P}+\mathrm{Q}+\mathrm{R}\) isTS EAMCET 2025 Hard
- A circle of radius 4 , drawn on a chord of the parabola \(y^2=8 x\) as diameter, touches the axis of the parabola. Then, the slope of the chord isTS EAMCET 2013 Hard
- \(\sinh { }^1 2+\cosh ^1 2-\tanh { }^1 \frac{2}{3}+\operatorname{coth}^1(-2)=\)TS EAMCET 2018 Medium
More PYQs from TS EAMCET
- In the interval \((-3,3)\) the function \(f(x)=\frac{x}{3}+\frac{3}{x}, x \neq 0\) is :TS EAMCET 2006 Easy
- If \(\alpha\) is a root of the equation \(x^2-x+1=0\), then \(\left(\alpha+\frac{1}{\alpha}\right)^3+\left(\alpha^2+\frac{1}{\alpha^2}\right)^3+\left(\alpha^3+\frac{1}{\alpha^3}\right)^3+\left(\alpha^4+\frac{1}{\alpha^4}\right)^3=\)TS EAMCET 2024 Easy
- Mustard gas among the following isTS EAMCET 2021 Medium
- \(x-2 y-6=0\) is a normal to the circle \(x^2+y^2+2 g x+2 f y-8=0\). If the line \(y=2\) touches this circle, then the radius of the circle can beTS EAMCET 2024 Medium
- The two lines and are such thatTS EAMCET 2021 Medium
- An electromagnetic wave having frequency \(4 \times 10^{14} \mathrm{~Hz}\) is passing through a small volume. The energy contained in this volume oscillates with frequencyTS EAMCET 2018 Easy