AP EAMCET · Maths · Application of Derivatives
Let \(a_n, a_{n-1}, \ldots, a_1, a_0 \in \mathbb{C}\) and \(f(x)=a_n x^n+a_{n-1} x^{n-1}+\ldots+\) \(a_1 x+a_0\) is a polynomial. If the polynomial \(f(x)\) is monic then
- A \(a_n \neq 0\)
- B \(a_n=1\)
- C \(a_n>0\)
- D \(\mathrm{a}_{\mathrm{n}} < 0\)
Answer & Solution
Correct Answer
(B) \(a_n=1\)
Step-by-step Solution
Detailed explanation
We have \(\mathrm{f}(\mathrm{x})=\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}}+\mathrm{a}_{\mathrm{n}-1} \times{ }^{\mathrm{n}-1}+\ldots . .+\mathrm{a}_1 \times \mathrm{a}_0\) here polynomial \(f(x)\) is a monic polynomial should be 1 \[ \Rightarrow \mathrm{a}_{\mathrm{n}}=1 \]
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
- The locus of centres of all circles which touch the line \(x=2 a\) and cut the circle \(x^2+y^2=a^2\) orthogonally isAP EAMCET 2017 Medium
- If \(\cos \alpha=\operatorname{sech} \beta\), then \(\beta=\)AP EAMCET 2025 Medium
- If all the letters of the word REPEAT are permuted in all possible ways and if the six letter permutations thus formed are arranged in the dictionary order, then the rank of the word REPEAT isAP EAMCET 2019 Easy
- A family of curves has the differential equation \(x y \frac{d y}{d x}=2 y^2-x^2\). Then, the family of curves isAP EAMCET 2010 Medium
- If the area of a circular sector of perimeter \(60 \mathrm{~m}\) is to be maximized, then its radius must be......... mAP EAMCET 2021 Easy
- If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\vec{b}=2 \hat{i}-3 \hat{j}-5 \hat{k}\), thenAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- The pair of straight lines represented by the equation \(3 d x^2-5 x y+\left(d^2-2\right) y^2=0\). If the lines are perpendicular to each other, for how many values of \(d\) this condition will be satisfied?AP EAMCET 2020 Easy
- If \(f(t)=\frac{1+\operatorname{cosec} t}{1-\operatorname{cosec} t}\) for \(0 < t < \frac{\pi}{2}\) and \(f^{\prime}(t)=f(t) g(t)\), then \(g(t)=\)AP EAMCET 2019 Easy
- In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(g\) \(=10 \mathrm{~ms}^{-2}\))
AP EAMCET 2019 Hard - A fair coin is tossed 100 times. The probability of getting tails an odd number of times isAP EAMCET 2012 Medium
- The correct statements regarding froth floatation method in metallurgy are
I. Used for the purification of sulphide ores
II. Used for the roasting of sulphide ores
III. It is based on the relative densities of gangue and ore particles
IV. It is based on the difference in the wetting properties of gangue and ore particles in frothing agent and waterAP EAMCET 2023 Easy - For is equal toAP EAMCET 2021 Medium