Question

Determine between which consecutive integers the real zeros of f(x)=2x^2-5x+1 are located.

a. between 0&1 and 1&2
b. between-1&0 and 2&3
c. between 0&1 and 2&3
d. between 1&2 and 2&3

Answer 1

If f(a) > 0 and f(b) < 0 for any a, b, then by the intermediate value theorem there is a root between a&b.

Answer 2

\[
\begin{matrix}x:&-1&0&1&2&3\\f(x):&8&1&-2&-1&4\\sign:&+&+&-&-&+\end{matrix}
\]
By my previous argument, there is a root between 0&1 and 2&3.