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Obtian all other zeroes of (x^(4)+4x^(3)...

Obtian all other zeroes of `(x^(4)+4x^(3)-2x^(2)-20x-15)` if two of its zeroes are ` :' sqrt(5)` and `-sqrt(5)` .

Text Solution

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`p(x) = x^(4) + 4x^(3) -2x^(2) - 20x -15`
`x^(2) - 5 ` is factor of p(x)
`therefore p(x)= (x^(2) -5) (x^(2) + 4x +3)`
Or`p(x) = (x^(2) -5)(x+3)(x+1)`
So, all the zeroes of p(x) are `sqrt(5),-sqrt(5),sqrt(3)` and `-1`
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