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Factor Theorem

If Z ^5, minu...

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If Z ^5, minus 32 can be factorised as linear factor of (Z- 2) (Z^2- pz + 4)(Z^2 - qz+4) find p^2+2q

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If the expression

z^{5} = 32

can be factorised into linear and quadratic factors over real coefficients as

(z^{5} - 32) = (z - 2) (z^{2} - p z + 4) (z^{2} - q z + 4)

, where p > q, then the value of

p^{2} - 2 q

p

q

are real so that the system of equations

p z + 4 y + z = 0, 2 y + 3 z = 1

3 x - q z = - 2

has infinite solutions then

\sqrt{q^{2} - p^{2}}

z + \frac{2}{z} = 4

,find the value of

z^{2} + \frac{4}{z^{2}}

Q. If a polynomial

a z^{3} + 4 z^{2} + 2 z - 4

z^{2} + 4 z + a

leave the same remainder divide by

(z - 3)

. Find the value of a.

z^{2} - z - 2

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