Question

Let $f\left(x\right)=x^4+3x+1,[-2,-1]$ then

• A. f has exactly two zeros in $[-2,-1]$
• B. f has exactly one zero in $[-2,-1]$
• C. f has at least one zero in $[-2,-1]$
• D. f has no zero in $[-2,-1]$

Answer 1

Answer: (B)

f has exactly one zero in $[-2,-1]$

Given, $f\left(x\right)=x^4+3x+1$
$f^{\prime }\left(x\right)=4x^3+3$, it has imaginary root it means $f^{\prime }\left(x\right)\ne 0$
it means it will cut only at once to x axis.
$f(-2)>0,f(-1)<0$
So, there exist a root in interval $[-2,-1]$