Question

Determine the value of a for which the polynomial 2x4-ax3+4x2+2x+1 is divisible by 1-2x

Answer 1

Please see the attachment

Answer 2

Answer:

We have...

=> 2x⁴ - ax³ + 4x² + 2x + 1 = p(x)  

Thus for the divisiblity of 1 - 2x  

=> 1 - 2x = 0  

=> x = 1/2  

Thus P(1/2) = 0

=> 2(1/2)⁴ - a(1/2)³ + 4(1/2)² + 2(1/2) + 1 = 0

=> 2(1/16) - a(1/8) + 4(1/4) + 1 + 1 = 0    

=> 1/8 - a/8 + 1 + 1 + 1 = 0

=> 1/8 - a/8 + 3 = 0

=> a/8 = 25/8

=> a = 25

Step-by-step explanation:

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