Question

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Answer 1

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Answer 2

x = - 1/√3                                  x = 1/√3

x + 1/√3 = 0 ---eq. 1                  x - 1/√3 = 0 ---eq.2

Multiplying eqs 1 & 2

(x +  1/√3) (x -  1/√3) = 0

x^2 - (1/√3)^2 = 0

x^2 - 1/3 = 0

Dividing p(x) by the equation above

Remainder = 0

Quotient = 3x^2 - 15x + 18

For finding remaining zeroes:

3x^2 - 15x + 18 = 0

divide by 3

x^2 - 5x +6 = 0

x^2 - 3x - 2x + 6  = 0

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

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

x - 2 = 0         x - 3 = 0

x = 2               x = 3

All the zeroes are:   1/√3, - 1/√3,  2, 3. : Ans

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