TS EAMCET · Maths · Complex Number
If \(\alpha, \beta\) are the roots of the equation \(x^2-2 \sqrt{3} x+4=0\) then \(\alpha^6+\beta^6=\)
- A 128
- B -64
- C 64
- D -128
Answer & Solution
Correct Answer
(D) -128
Step-by-step Solution
Detailed explanation
Given equation \(x^2-2 \sqrt{3} x+4=0\) with \(\alpha \& \beta\) roots of the equation. \(\begin{aligned} & \alpha+\beta=\frac{-b}{a}=2 \sqrt{3} \\ & \alpha \beta=\frac{c}{a}=4 \end{aligned}\) Now, \(\left(\alpha^6+\beta^6\right)=\left(\alpha^2\right)^3+\left(\beta^2\right)^3\)…
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
- The point on the line which is equidistant from the points and is-TS EAMCET 2021 Easy
- If \(A(x)=\left|\begin{array}{ccc}1 & 2 & 3 \\ x+1 & 2 x+1 & 3 x+1 \\ x^2+1 & 2 x^2+1 & 3 x^2+1\end{array}\right|\),
then \(\int_0^1 A(x) d x\) equalsTS EAMCET 2015 Easy - The value of \(\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}\) is :TS EAMCET 2003 Easy
- \(\begin{aligned} & \text { If } 5(f(x))^2=x f(x)+30 \text { and } \ & \int \frac{\left(3 x^3+\left(1-30 x^2\right) f(x)\right)}{(10 f(x)-x)\left(x^3-f(x)\right)^2} d x \ & =\frac{A}{B x^3+D f(x)}+C \text { then } A+B+D=\end{aligned}\)TS EAMCET 2020 Hard
- \[ \int_0^2 \frac{x}{(2-x)^{\frac{3}{4}}} d x= \]TS EAMCET 2023 Medium
- The approximate value of \(\sec 59^{\circ}\) obtained by taking \(1^{\circ}=\) 0.0174 and \(\sqrt{3}=1.732\) isTS EAMCET 2024 Easy
More PYQs from TS EAMCET
- Consider the following two statements, \(A\) and \(B\) and identify the correct answer given below: A. Nuclear density is same for all nuclei B. Radius of the nucleus \(R\) and its mass number \(A\) are related as \(\sqrt{A} \propto R^{1 / 6}\).TS EAMCET 2004 Easy
- Which of the following is not a periodic property?TS EAMCET 2021 Easy
- A water drop breaks into 64 identical droplets of each surface area \(10^{-7} \mathrm{~m}^2\). If the surface tension of water is \(0.07 \mathrm{Nm}^{-1}\), the increase in the surface energy in the process isTS EAMCET 2023 Easy
- Two charged identical metal spheres \(A\) and \(B\) repel each other with a force of \(3 \times 10^{-5} \mathrm{~N}\). Another identical wncharged sphere \(C\) is touched with sphere \(A\) and then it is placed mid-way between \(A\) and \(B\). Then, the magnitude of net force on \(C\) isTS EAMCET 2016 Medium
- Identify ' \(B\) ' in the following reaction \(\begin{aligned} & \mathrm{CH}_2=\mathrm{CH}_2+\mathrm{HCl} \stackrel{\text { anhy } \cdot \mathrm{AlCl}_3}{\longrightarrow} A+2[\mathrm{H}] \ & \stackrel{\mathrm{Zn}-\mathrm{Cu}}{\underset{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}}{\longrightarrow}} \mathrm{B}+\mathrm{HCl}\end{aligned}\)TS EAMCET 2007 Medium
- An electrolyte of a polymer-salt complex of poly (ethylene oxide) - is shaped into a free standing circular film of diameter and a thickness of When it is sandwiched between 2 stainless steel circular electrodes of the same diameter, this cell exhibits a conductance of What is the specific conductivity of the electrolyte?TS EAMCET 2019 Hard