X^3+bx^2-4x-20=0
find b
find the roots

p(x) = x^3 - 5x^2 - 4x + 20

Step-by-step explanation:

1, - 1, 2, - 2, 4, - 4, 5, - 5, 10, - 10, 20, - 20

P(2) = 2^3 - 5 × 2^2 - 4 × 2 + 20

= 8 - 20 - 8 + 20 = 0,

so, 2 is one of its roots (zeros)

So,

x - 2 is one of the factors of p(x)

So, on dividing p(x) by x - 2 we get

P(x) = (x - 2) (x^2 - 3x - 10)

= (x - 2) (x^2 - 5x + 2x - 10)

= (x - 2) {x (x - 5) + 2 (x - 5)}

= (x - 2) {(x - 5) (x + 2)}

P(x) = (x - 5) (x - 2) (x + 2)

For zeros, let p(x) = 0

=> (x - 5) (x - 2) (x + 2) = 0

Either

(x - 5) = 0

Or

(x - 2) = 0

Or

(x + 2) = 0

So, x = 5, 2, - 2

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