If (1 – 2x) is a factor of P(x)=2x4 - ax³ + 4x² +2x +1 find the value of a.
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Hey freind, here is your answer --
p(x) = 2x^4 - ax³ + 4x² + 2x + 1
g(x) = 1 - 2x
g(x) = 0
1 - 2x = 0
x = 1 /2
Putting x = 1 /2 in p(x)
p(1 /2) = 2(1 /2)^4 - a(1 /2)³ + 4(1 /2)² +2(1 /2) +1
p(1 /2) = 2(1 / 16) - a(1 / 8) + 4(1 /4) +2(1 /2) +1
p(1 /2) = 1 / 8 - 1 / 8a + 1 +1 +1
p(1 /2) = 1 / 8 - 1a / 8 + 8 / 8 + 8 / 8 + 8 / 8
As ( 1 - 2x ) is factor of p(x) so p(1 /2) = 0
0 = 1 - a + 8 + 8 + 8 / 8
0 * 8 = 25 - a
0 + a = 25
a = 25
Hope it helps
p(x) = 2x^4 - ax³ + 4x² + 2x + 1
g(x) = 1 - 2x
g(x) = 0
1 - 2x = 0
x = 1 /2
Putting x = 1 /2 in p(x)
p(1 /2) = 2(1 /2)^4 - a(1 /2)³ + 4(1 /2)² +2(1 /2) +1
p(1 /2) = 2(1 / 16) - a(1 / 8) + 4(1 /4) +2(1 /2) +1
p(1 /2) = 1 / 8 - 1 / 8a + 1 +1 +1
p(1 /2) = 1 / 8 - 1a / 8 + 8 / 8 + 8 / 8 + 8 / 8
As ( 1 - 2x ) is factor of p(x) so p(1 /2) = 0
0 = 1 - a + 8 + 8 + 8 / 8
0 * 8 = 25 - a
0 + a = 25
a = 25
Hope it helps
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