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

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