Question

find all zeroes of the polynomial x^3+3x^2-2x-6 ,if two of it's zeroes are -√2 and √2

Answer 1

your answer is -3
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Answer 2

If two zeroes are √2 and -√2 so, the factor will be

(x-√2)(x+√2)=0

⇒x²-2=0

now, dividing the expression with this,

x²-2)x³+3x²-2x-6(x+3

x³-2x

- +

+3x²-6

+3x²-6

- +

x

so, x³+3x²-2x-6 = (x²-2) (x+3)

All the zeroes are = -√2 , +√2 , -3

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