If one of the zeroes of the cubic polynomial x3 + ax2 + bx is –1, then the product of the other two zeroes isSelect an answerA0Bb – a – 1Ca – b + 1 Da – b –1
Question
If one of the zeroes of the cubic polynomial x3 + ax2 + bx is –1, then the product of the other two zeroes isSelect an answerA0Bb – a – 1Ca – b + 1 Da – b –1
Solution
The sum of the zeroes of a cubic polynomial x³ + ax² + bx + c is given by -a. The product of the zeroes taken two at a time is given by b. The product of all the zeroes is given by -c.
Given that one of the zeroes is -1, let's denote the other two zeroes as p and q.
According to Vieta's formulas, the sum of the zeroes p, q, and -1 is equal to -a. Therefore, we have:
p + q - 1 = -a => p + q = -a + 1
The product of the zeroes taken two at a time is given by b. Therefore, we have:
pq + (-1)p + (-1)q = b => pq - p - q = b => pq = b + p + q => pq = b + (-a + 1) (substituting p + q = -a + 1) => pq = b - a + 1
Therefore, the product of the other two zeroes is b - a + 1. So, the correct answer is C: a - b + 1.
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