Question

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

Answer:

a = 25

Step-by-step explanation:

P(x) = 2x⁴ - ax³ + 4x² + 2x + 1

-2x + 1 = 0

-2x = -1

-x = -1/2

x= 1/2

P(1/2) = 2(1/2)⁴ - a(1/2)³ + 4(1/2)² + 2(1/2) + 1

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

= 1/8 - a/8 + 1 + 1 + 1

= 1 - a + 8 + 8 + 8/8

25 - a/8 = 0

25 - a = 0

- a = -25

∴ a = 25

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