A coprime rational game 4'

Algebra Level 4

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 fourth smallest possible value of $a_{0}+a_{n}$ .

For more such problems, click here .

The answer is 13.

1 solution

Prince Loomba
Jun 17, 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 $a_{n}$ . One more thing is there that $a_{0} \quad and \quad a_{n}$ are coprime that is x cannot be a multiple of 3 and y cannot be multiple of 2 . Thus we need fourth smallest value of $2x+3y$ , which is obtained when x and y are 5 and 1 respectively. Hence answer is $10+3=13$

A coprime rational game 4'

For more such problems, click here .

The answer is 13.

1 solution

0 pending reports