TS EAMCET · Maths · Complex Number
If \(\alpha, \beta\) are the roots of \(1+x+x^2=0\), then the value of \(\alpha^4+\beta^4+\alpha^{-4} \beta^{-4}\) is
- A 0
- B 1
- C -1
- D 2
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} 1+x+x^2 & =0 \\ \Rightarrow \quad x & =\frac{-1 \pm \sqrt{1-4}}{2} \Rightarrow x=\frac{-1 \pm \sqrt{3} i}{2} \\ \Rightarrow \quad x & =\omega, \omega^2 \end{aligned} \] It is given that, \(\alpha, \beta\) are the roots of the equation \(1+x+x^2=0\).…
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 perpendicular distance from the origin to the plane containing the points having position vectors isTS EAMCET 2021 Easy
- For the equation \(x^4+x^3-4 x^2+x-1=0\) the ratio of the sum of the squares of all the roots to the product of the distinct roots isTS EAMCET 2020 Medium
- The tangents drawn from a point \((2,-1)\) touch the circle \(x^2+y^2+4 x-2 y+1=0\) at the points A and B. If C is the centre of the circle, then the area (in sq. units) of the triangle ABC isTS EAMCET 2025 Medium
- If \(X\) is a binomial variate with the range \(\{0,1,2,3,4,5,6\}\) and \(P(X=2)=4 P(X=4)\), then the parameter \(p\) of \(X\) isTS EAMCET 2009 Easy
- If and the angle between and is then the area of the triangle (in square units) with and as two of its sides isTS EAMCET 2021 Easy
- A normal chord PQ drawn at a point P on the parabola \(y^2=5 x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord isTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- If \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{\tan \mathrm{x}}+(\tan \mathrm{x})^{\mathrm{x}}\), then \(\mathrm{f}^{\prime}\left(\frac{\pi}{4}\right)=\)TS EAMCET 2023 Medium
- If the circle \(S=x^2+y^2+2 g x+2 f y+c=0\) cuts each of the three circles \(x^2+y^2+4 x+4 y+7=0, x^2+y^2-4 x+\) \(4 y+7=0\) and \(x^2+y^2-4 x-4 y+7=0\) orthogonally, then the equation of the tangent drawn at the point \((\sqrt{3}, 2)\) to the circle \(\mathrm{S}=0\) isTS EAMCET 2023 Medium
- In the balanced equation of the following reaction, the ratio of isTS EAMCET 2021 Medium
- If \(4 x+y+p=0(p>0)\) is a tangent to the ellipse \(x^2+3 y^2=3\) and \(16 x+q y+14=0(q>0)\) is a normal to the ellipse \(x^2+8 y^2=33\), then \(p+q=\)TS EAMCET 2018 Medium
- Match the following:
The correct answer is:
TS EAMCET 2019 Easy - If the equation of the circle passing through the points \((-1,0),(-1,1),(1,1)\) is \(a x^2+a y^2+2 g x+2 f y-2=0\) then \(a=\)TS EAMCET 2025 Medium