Login/Sign Up
Home » It is given that is one of the zeroes of the polynomial . Find all the zeroes of the given polynomial.
It is given that -1 is one of the zeroes of the polynomial x^{3}+2 x^{2}-11 x-12. Find all the zeroes of the given polynomial.
CBSE | Class 10 | Excercise 2B | Maths | Polynomials | RS Aggarwal
It is given that -1 is one of the zeroes of the polynomial x^{3}+2 x^{2}-11 x-12. Find all the zeroes of the given polynomial.

Let f(x)=x^{3}+2 x^{2}-11 x-12

Since -1 is a zero of f(x),(x+1) is a factor of f(x).

On dividing \mathrm{f}(\mathrm{x}) by (\mathrm{x}+1), we get

    \[\begin{aligned} &f(x)=x^{3}+2 x^{2}-11 x-12 \\ &=(x+1)\left(x^{2}+x-12\right) \\ &=(x+1)\left\{x^{2}+4 x-3 x-12\right\} \\ &=(x+1)\{x(x+4)-3(x+4)\} \\ &=(x+1)(x-3)(x+4) \\ &\begin{aligned} \therefore f(x)=0 & \Rightarrow(x+1)(x-3)(x+4)=0 \\ & \Rightarrow(x+1)=0 \text { or }(x-3)=0 \text { or }(x+4)=0 \\ & \Rightarrow x=-1 \text { or } x=3 \text { or } x=-4 \end{aligned} \end{aligned}\]

Thus, all the zeroes are -1,3 and -4.

i

More Material