Question

If $f\left(x\right)$ is a polynomial such that $f\left(a\right)f\left(b\right)<0$, then number of zeros lieing between $a$ and $b$ is

• A. $one$
• B. $atleastone$
• C. $two$
• D. $atmost2$

Answer 1

The correct option is B $atleastone$

$f\left(x\right)\text{is a polynomial}$

$f\left(a\right)f\left(b\right)<0$ implies that one of them must be negative and other must be positive.

So the graph of $f\left(x\right)$ must be on the both sides

of the $x$ axis i.e above or below the $x$ -axis.

i. e. graph of $f\left(x\right)$ should cut the $x$ -axis

at least once in between $a$ and $b$.

Therefore, no. of zeroes of $f\left(x\right)$ between $a$

and $b$ is at least one.