One solution of the equation x^3 + 5x^2 + 5x - 2 = 0
is -2. Find the sum of the remaining solutions.
Hi
No, that's not what Moo meant. The degree of is 3 which means that this polynomial has 3 roots. (they can be real or complex numbers) Let's denote these roots by and and factor the polynomial : . Expanding this expression, what do we get ? Let's see :
What we learn from this is that the coefficient of is the opposite of the sum of the three roots. As this coefficient equals 5, ( ) we have . Knowing that one of the roots is -2, you can solve this for the sum of the two remaining roots.
What Moo meant is that if the polynomial were then the sum of the roots would have been equal to .
Is it clearer ?