A rational game

Algebra Level 3

A polynomial with integer coefficients $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}$ , with $a_{n}$ and $a_{0}$ being coprime positive integers , has one of the roots $\dfrac{2}{3}$ . Find the smallest possible value of $a_{0}+a_{n}$ . For complete set, click here

The answer is 5.

1 solution

Prince Loomba
Jun 16, 2016

$a_{0}=2x$ and $a_{n}=3y$ because according to rational roots theorem, $2$ is factor of $a_{0}$ and $3$ is factor of $a_{n}$ . Thus we need smallest value of $2x+3y$ , which is obtained when x and y are 1 and 1 respectively. Hence answer is $2+3=5$

A rational game

The answer is 5.

1 solution

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