Obtain all the zeros of the polynomial x4 +4x3 -2x2 -20x-15, if two of

1.	Obtain all the zeros of the polynomial x4 +4x3 -2x2 -20x-15, if two of its zeroes are √5 and −√5.
Answer» p(x) = x⁴ + 4x³-2x² - 20x -15 x²- 5 is factor of p(x) ∴ p(x) = (x² -5) (x² + 4x +3) or p(x) = (x² -5) (x -3) (x +1) So, all the zeroes of p(x)(are √5, −√5, −3 and −1.

Obtain all the zeros of the polynomial x4 +4x3 -2x2 -20x-15, if two of its zeroes are √5 and −√5.

Answer»

p(x) = x⁴ + 4x³-2x² - 20x -15

x²- 5 is factor of p(x)

∴ p(x) = (x² -5) (x² + 4x +3)

or p(x) = (x² -5) (x -3) (x +1)

So, all the zeroes of p(x)(are √5, −√5, −3 and −1.

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Obtain all the zeros of the polynomial x4 +4x3 -2x2 -20x-15, if two of its zeroes are √5 and −√5.

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