Q30 of 40 Page 1

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

-3 & -1


Let, P(x) = x4 + 4x3 – 2x2 – 20x – 15


Zeros of P(x) are √5 and -√5.


Therefore, (x - √5) & (x + √5) are factors of P(x).


Therefore, (x - √5).(x + √5) = (x2 – 5) is also factor of P(x).


Dividing P(x) by (x2 – 5),



To get zeros of P(x),


x2 + 4x + 3 = 0


∴ x2 + 3x + x + 3 = 0


∴ x(x + 3) + 1(x + 3) = 0


∴ (x + 3) .(x + 1) = 0


∴ x = -3 or x = -1


Hence, zeros of P(x) are √5, -√5, -3 & -1.


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