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A non-zero polynomial $f(x)$ of degree 3 has roots at $x=1$, $x=2$ and $x=3$. Which one of the following must be TRUE?

1. $f(0)f(4)< 0$
2. $f(0)f(4)> 0$
3. $f(0)+f(4)> 0$
4. $f(0)+f(4)< 0$

The roots are $x=1, x=2$, and $x=3.$

So, polynomial is $f(x) = (x-1)(x-2)(x-3)$

$f(0) = -6, f(4) = 6$

So, $f(0)f(4) < 0$.

Correct Answer: $A$

here we just need to draw possible graphs,no need to solve the whole equation and get values.

by

Why draw graph when you can solve it directly? f(0) value is there already, f(4) can be calculated as we have f(x). ( f is of degree 3 all roots are there so we can get f(x) )
This should be the best solution because it cover both case when leading coefficient is positive or negative.nice @shifali
Isn't this the well known wavy curve method?

### 1 comment

nice explanation @regina