AP EAMCET · Maths · Quadratic Equation
The sum of the fourth powers of the roots of the equation \(x^3+x+1=0\) is
- A \(-2\)
- B \(-1\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Given equation is \(x^3+x+1=0\) On comparing with \(x^3+p_1 x^2+p_2 x+p_3=0\), we get Now, \[ p_1=0, p_2=1, p_3=1 \]…
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
- If \(P_1, P_2\) and \(P_3\) are the lengths of the altitudes drawn from the vertices \(A, B\) and \(C\) of \(\triangle A B C\) respectively, then \(\frac{\cos A}{P_1}+\frac{\cos B}{P_2}+\frac{\cos C}{P_3}=\)AP EAMCET 2023 Medium
- The equation of the circle with \((1,1)\) as centre and which cuts a chord of length \(4 \sqrt{2}\) units on the line \(x+y+1=0\) isAP EAMCET 2017 Medium
- Let \(\bar{a}=2 \bar{i}+\bar{j}+3 \bar{k}, \bar{b}=3 \bar{i}+3 \bar{j}+\bar{k}\) and \(\bar{c}=\bar{i}-2 \bar{j}+3 \bar{k}\) be three vectors. If \(\bar{r}\) is a vector such that \(\overline{\mathrm{r}} \times \overline{\mathrm{a}}=\overline{\mathrm{r}} \times \overline{\mathrm{b}}\) and \(\overline{\mathrm{r}} \cdot \overline{\mathrm{c}}=18\), then the magnitude of the orthogonal projection of \(4 \overline{\mathrm{i}}+3 \overline{\mathrm{j}}-\overline{\mathrm{k}}\) on \(\overline{\mathrm{r}}\) isAP EAMCET 2025 Hard
- The normal to the curve \(x=a(1+\cos \theta)\), \(y=a \sin \theta\) at \(\theta\) always passes through a fixed point, then the fixed point isAP EAMCET 2022 Medium
- The discrete random variables and are independent from one another and are defined as and . Then the sum of the variances of and isAP EAMCET 2022 Medium
- The coefficient of \(x^4\) in the expansion of \(\frac{1}{(1-x)(1-2 x)(1-3 x)}\) isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.AP EAMCET 2022 Easy - If \(\omega\) is the cube root of unity \(\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+a \omega^2}=\)AP EAMCET 2024 Easy
- One mole of 2-methylbuta-1, 3-diene on ozonolysis givesAP EAMCET 2022 Easy
- A full wave rectifier circuit is operating from 50 Hz mains, the fundamental frequency in the ripple output will beAP EAMCET 2024 Easy
- At \(\mathrm{T}(\mathrm{K})\), the vapour pressure of pure benzene and toluene are 75 and 22 mm Hg respectively. 23.4 g of benzene and 64.4 g of toluene are mixed to form an ideal solution. If the vapours are in equilibrium with the liquid mixture, the mole fraction of toluene in vapour phase is (At.wt of \(\mathrm{C}=12 ; \mathrm{H}=1\) )AP EAMCET 2025 Medium
- A body projected from the ground reaches a point \(X\) in its path after 3 seconds and from there it reaches the ground after further 6 seconds. The vertical distance of the point \(X\) from the ground is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2016 Medium