Question

8. If root 3 and -root 3 - are two of the zeroes.
of the polynomial f(x) = x^ 4 _ 3x² _ x² + 9x -6
Find the other zeroes.​

Answer 1

Answer:

$p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ p(x) = {x}^{2} - ( \sqrt{3} + \ \sqrt{ - 3} )x + ( \sqrt{3} \times \sqrt{ - 3} ) \\ p(x) = \ {x}^{2} - 0x - 3 \\ p(x) = {x}^{2} - 3$

$g(x) = {x}^{2} + 0x - 1 \\ \: \: \: \: \: \: \: \: \: = (x - 1)(x + 1) \\ (x - 1)=0 \\ \: \: \: \: \: \: \: \: \: \: \: \:x = 1 \\ (x + 1) = 0 \\ \: \: \: \: \: \: \: \: \: \: \: x = ( - 1)$

Therefore,other two zeroes are 1 and (-1).

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