Question

If f(x) =0 has a root between a & b then f(a) & f(b) are of __________ signs.

Answer 1

Answer:

opposite

Step-by-step explanation:

the values will be of opposite signs

Answer 2

Answer:

$f(a)$ or  $f(b)$ are of opposit signs always.

Step-by-step explanation:

Given equation is $f(x)=0$ and it is given that $f$ has a root between $a$ and $b$ then the graph of $f$ intersects $x-$axis at that point. So, one of $f(a)$ or  $f(b)$  lies below $x-$axis and other above $x-$axis.

If a value lies below $x-$axis then it is negative and if it lies above $x-$axis then it is positive.

Hence, one of $f(a)$ or  $f(b)$  is either positive or negative i.e., they are of opposite sign.