If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is –1 then the product of the other two zeros is ______.

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If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is –1 then the product of the other two zeros is 1 – a + b. Explanation: Since –1 is a zero of x3 + ax2 + bx + c, we have (–1)3 + a $\times$ (–1)2 + b $\times$ (–1) + c = 0 $\Rightarrow$ a – b + c – 1 = 0 $\Rightarrow$ c = 1 – a + b Also, product of all zeros is given by $\alpha$$\beta$ $\times$ (–1) = –c $\Rightarrow$ $\alpha$$\beta$ = c $\Rightarrow$ $\alpha$$\beta$ = 1 – a + b

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