Root problem

Algebra Level 4

If $p$ , $q$ and $r$ are real roots of equation $x^3-9x^2+24x+c=0$ , find the minimum value of $\lfloor p \rfloor + \lfloor q \rfloor +\lfloor r \rfloor$ .

Notation: $\lfloor \cdot \rfloor$ denotes the floor function .

The answer is 7.

1 solution

Prajwal Krishna
Nov 17, 2016

p+q+r = 9

[p]+{p}+[q]+{q}+[r]+{r} = 9

[p]+[q]+[r] = 9 - ( {p}+{q}+{r})

0 <= {x}< 1

So 0 <= {p}+{q}+{r} <3

Hence minimum integral value of [p]+[q]+[r] = 7

Root problem

The answer is 7.

1 solution

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