Question

5) What should be added in the polynomial 3x4 – 4x3 -6x2 +4 that it is completely divisible by x2-2

Answer 1

Answer

Since The given equation is exactly divisible by

x-2,it means that x-2 is the factor of the given equation and x=2 is one of the roots of the equation.

x5 - 3x4 –ax3 + 3ax2 + 2ax + 4

Putting x=2 in the above equation,it will become 0 since 2 is its root.

(2)^5-3(2)^4-a(2)^3+3a(2)^2+2a(2)+4=0

or,32-48-8a+12a+4a+4=0

or,8a-8=0

or,a=1

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