search
Log In
0 votes

A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$. Which one of the following conditions must be satisfied?

  1. $\varphi \left ( s \right ) = 0$ at all the three values of $s$ satisfying $s^{3}+ \sigma ^{3}=0$
  2. $\varphi \left ( s \right ) = 0, \frac{d\varphi \left ( s \right )}{ds} = 0$, and $\frac{d^{2}\varphi \left ( s \right )}{ds^{2}} = 0$ at  $s = -\sigma$
  3. $\varphi \left ( s \right ) = 0, \frac{d^{2}\varphi \left ( s \right )}{ds^{2}} = 0$, and $\frac{d^{4}\varphi \left ( s \right )}{ds^{4}} = 0$ at  $s = -\sigma$
  4. $\varphi \left ( s \right ) = 0,$ and $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$
in Others 27.4k points
edited by

Please log in or register to answer this question.

Answer:

Related questions

1 vote
1 answer
Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).
asked Feb 15 in Spatial Aptitude Arjun 27.4k points
0 votes
0 answers
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson’s rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined as $e = 100\times \left ( I_{e} - I_{S}\right )/I_{e}$. The value of $e$ is $2.5$ $3.5$ $1.2$ $0$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
asked Feb 15 in Others Arjun 27.4k points
...