AP EAMCET · Maths · Quadratic Equation
If \(f(x) \in \mathbf{Q}[x]\) be a non-zero polynomial such that all its roots are irrational, then the degree of \(f(x)\) is
- A an even number
- B an odd number
- C 0
- D can't determine
Answer & Solution
Correct Answer
(A) an even number
Step-by-step Solution
Detailed explanation
Irrational roots exist in pair So, the degree of \(f(x)\) will be an even number
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 there is an error of \(\pm 0.04 \mathrm{~cm}\) in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is \(10 \mathrm{~cm}\), isAP EAMCET 2014 Hard
- \(\cos 66^{\circ}+\sin 84^{\circ}=\)AP EAMCET 2019 Medium
- In an ellipse, two vertices are \((5,0)\) and \((0,-4)\). Then the equation of the ellipse isAP EAMCET 2020 Easy
- If and are the roots of the quadratic equation , then the equation whose roots are is given by ______AP EAMCET 2021 Medium
- The sum of the fourth powers of the roots of the equation \(x^3+x+1=0\) isAP EAMCET 2008 Medium
- The polynomial equation of degree 4 having real coefficients with three of its roots as \(2 \pm \sqrt{3}\) and \(1+2 i\), isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- A discrete random variable \(X\) has the distribution \(B(15, p)\). Given that \(\operatorname{Var}(X)=3.15\). Then, the two possible values of \(p\) areAP EAMCET 2022 Medium
- A toy of mass \(20 \mathrm{~g}\) at rest acquires a velocity \((3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}) \mathrm{ms}^{-1}\) in 2 seconds. Then the power of the toy isAP EAMCET 2023 Medium
- An electron having kinetic energy of \(100 \mathrm{eV}\) circulates in a path of radius \(10 \mathrm{~cm}\) in a magnetic field. The magnitude of magnetic field \(|\mathbf{B}|\) is approximately [Mass of electron \(=0.5 \mathrm{MeV} \mathrm{c}^{-2}\), where \(\mathrm{c}\) is the velocity of light].AP EAMCET 2022 Easy
- A thin flexible wire of length \(L\) is connected to two adjacent fixed points and carries a current \(I\) in the clockwise direction as shown. When the system is put in uniform magnetic field of strength \(B\) going into the plane of the paper, the wire take the shape of a circle. The tension in the wire, after acquiring the circular shape is
AP EAMCET 2021 Hard - The number of molecules having lone pair of electrons on central atom in the following is
\(\mathrm{BF}_3,~ \mathrm{SF}_4,~ \mathrm{SiCl}_4,~ \mathrm{XeF}_4,~ \mathrm{NCl}_3,~ \mathrm{XeF}_6,~ \mathrm{PCl}_5,~ \mathrm{HgCl}_2,~ \mathrm{SnCl}_2\)AP EAMCET 2025 Medium - The efficiency of a Carnot's heat engine is \(\frac{1}{3}\). If the temperature of the source is decreased by \(50^{\circ} \mathrm{C}\) and the temperature of the sink is increased by \(25^{\circ} \mathrm{C}\), the efficiency of the engine becomes \(\frac{3}{16}\). The initial temperature of the sink isAP EAMCET 2025 Medium