Question

find the zeros of cubic polynomial |)-x³ ||)x²-x³ |||)x³-5x²+6x without drawing the graph of the polynomial​

Answer 1

Step-by-step explanation:

Note:

1) For finding the zeros of the polynomial, we should equate it to zero.

2) The maximum number of zeros of a polynomial is equal to the degree of the polynomial.

Solution:

1) For zeros of the polynomial (-x^3)

=> -x^3 = 0

=> x^3 = 0

=> x = 0,0,0

Thus, the zeros of the given polynomial are , x=0,x=0,x=0

Here, all the zeros of the polynomial are equal.

2) For zeros of the polynomial (x^2-x^3)

=> x^2-x^3 = 0

=> x2(1-x) = 0

=> x = 0,0,1

Thus, the zeros of the given polynomial are , x=0,x=0,x=1

Here, the two zeros are equal and third one is different.

3) For zeros of the polynomial

(x^3 - 5x^2 + 6x)

=> x^3 - 5x^2 + 6x = 0

=> x{x^2 - 5x + 6} = 0

=> x{x^2 - 3x - 2x + 6} = 0

=> x{x(x-3)-2(x-3)} = 0

=> x(x-3)(x-2) = 0

=> x = 0,2,3

Thus, the zeros of the given polynomial are , x=0,x=2,x=3

Here, all the three zeros are distinct.

Answer 2

Answer:

I hope that this answer helps you