The polynomial P(x)=x^(3)+ax^(2)+bx+c has the property that the mean of its roots, the product of its roots, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=P(x) is 2, The value of P(1) is

The polynomial P(x)=x^(3)+ax^(2)+bx+c has the property that the mean o

1.	The polynomial P(x)=x^(3)+ax^(2)+bx+c has the property that the mean of its roots, the product of its roots, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=P(x) is 2, The value of P(1) is
Answer» `0` `-1` `2` `-2` Solution :The `y`-INTERCEPT is at `x=0`, so we have `c=2`, meaning that the product of the roots is `-2`. We know that `-a` is the sum of the roots. The average of the roots is equal to the product, so the sum of the roots is `-6`, and `a=6`. FINALLY, `1+a+b+c=2` as well, so we have `1+6+b+2=-2` `impliesb=-11` `:.P(x)=x^(3)+6X^(2)-11x+2` `:.P(1)=1+6-11+2=-2`

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The polynomial P(x)=x^(3)+ax^(2)+bx+c has the property that the mean of its roots, the product of its roots, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=P(x) is 2, The value of P(1) is

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