A non-zero polynomial with real coefficients has the property tha… - Vidyadip

MCQ

A non-zero polynomial with real coefficients has the property that $f''(x) f'(x) = f(x)$ . Then the value of $f'''(x)$ is

✓
$0$
B
$-1$
C
$f(x)$
D
$f'(x)$

✓

Answer

Correct option: A.

$0$

a
Let degree of $f(x)=n$

Degree of $f^{\prime}(x)=n-1$

degree of $f^{\prime \prime}(x)=n-2$

$\therefore f^{\prime \prime}(x) f^{\prime}(x)=f(x)$

Then $(n-2)+(n-1)=n$

${2 n-3=n} $

${n=3}$

Now let $f(x)=a x^{3}+b x^{2}+c x+d$

Then $f^{\prime \prime \prime}(x)=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$AB,BC$ are diagonals of adjacent faces of a rectangular box with its centre at the origin, its edges parallel to the co-ordiantes axes.If the angles $BOC, COA$ and $AOB$ are $\alpha,\beta$ and $\gamma$ respectively, then $cos\,\,\alpha + cos\,\,\beta + cos\,\,\gamma$ is-

The area of the region enclosed between the parabolas $y ^{2}=2 x -1$ and $y ^{2}=4 x -3$ is

A straight line through origin $O$ meets the lines $3y= 10 - 4x$ and $8x + 6y+ 5 = 0$ at points$ A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio

If the general solution of the differential equation $y' = \frac{y}{x} + \phi \left( {\frac{x}{y}} \right)$ , for some function $\phi $, is given by $y \ln \,\left| {cx} \right| = x$, where $c$ is an arbitrary constant, then $\phi \,(2)$ is equal to:

$\int\limits_{ - 2}^\pi {\frac{{{{\sin }^2}x}}{{\left[ {\frac{x}{\pi }} \right] + \frac{1}{2}}}} \,dx$ is equal to (where $[·]$ denotes the greatest integer function)

The interval in which the function ${x^2}{e^{ - x}}$ is non decreasing, is

A die is loaded such that the probability of throwing the number $'i'$ is proportional to it's reciprocal. Then the probability that $3$ appears in a single throw is

If $a_1, a_2, a_3, …….$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first $15$ terms of this $A.P.$ is

If $A\,(1\,,\,\,2,\,\, - 1)$ and $B( - 1,\,\,0,\,\,1)$ are given, then the co-ordinates of $P $ which divides $AB$ externally in the ratio $1:2$, are

For all real values of $m$, the straight line $y = mx +\sqrt {9\,{m^{2\,}}\, - \,\,4} $ is a tangent to the curve :