If two zeros of the polynomial p(x) = x^3 + x | vedclass

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(B) Let the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ be $\alpha, \beta,$ and $\gamma$.Given: $\alpha = \sqrt{5}$,$\beta = -\sqrt{5}

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-$1$

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(B) Let the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ be $\alpha, \beta,$ and $\gamma$.Given: $\alpha = \sqrt{5}$,$\beta = -\sqrt{5}$,and we need to find $\gamma$.According to the relationship between zeros and coefficients of a cubic polynomial,the sum of the zeros is given by:$\alpha + \beta + \gamma = -\frac{b}{a}$From the polynomial $p(x) = x^3 + x^2 - 5x - 5$,we have $a = 1$ and $b = 1$.Substituting the values:$\sqrt{5} + (-\sqrt{5}) + \gamma = -\frac{1}{1}$$0 + \gamma = -1$$\gamma = -1$Thus,the third zero is $-1$.

If two zeros of the polynomial $p(x) = x^3 + x^2 - 5x - 5$ are $\sqrt{5}$ and $-\sqrt{5}$,then the third zero is . . . . . . .

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