Question

It is given that -1 is one of the zeros of the polynomial x³+2x²-11x-12.Find the all zeros of given polynomial.

Answer 1

Answer:

-1^3+2×-1^2-11×-1-12

-1+2×1+11-12

-1+2+11-12

-13+13

=0

Step-by-step explanation:

hope it helps you

Answer 2

Answer:

l

$let \: f(x) = {x}^{3} + {2x}^{2} - 11x - 12 \\ since \: - 1 \: is \: a \: zero \: of \: f(x) \: so \: (x + 1) \: is \: factor \: of \: f(x). \\ o n \: dividing \: f(x) \: by \: (x + 1) \: we \: get$

x+1) x³+2x²-11x-12(x²+x-12

x³+x²

- -

_________

x²-11x

x²+x

- -

_________

-12x-12

-12x-12

+ +

_________

F(x) = x³+2x-11x-12= (x+1) (x²+x-12)

= (x+1) (x²+4x-3x-12)

= (x+1) {x(x+4)-3(x+4) }

= (x-1) (x-3) (x+4)

F(x) =0

(x-1) (x-3) (x+4)=0

(x-1) =0 or (x-3) =0 or (x+4) =0

x=1 or x= 3 or x= -4

Thus the other zeros are -4 and 3.

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