A rational game 3

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 positive integers , has one of the roots $\dfrac{2}{3}$ . Find the third smallest possible value of $a_{0}+a_{n}$ .

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The answer is 8.

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 $a_{n}$ . Thus we need third smallest value of $2x+3y$ , which is obtained when x and y are 1 and 2 respectively. Hence answer is $2+6=8$

nice solution..+1

Ayush G Rai - 4 years, 12 months ago

Thanks ayush

Prince Loomba - 4 years, 12 months ago

A rational game 3

For complete set, click here .

The answer is 8.

1 solution

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