Q. 214.0( 8 Votes )

Find the value of m so that 2x – 1 be a factor of 8π‘₯4 + 4π‘₯3βˆ’16π‘₯2 + 10π‘₯ + π‘š.

Answer :

let p(x) = 8x4 + 4x3βˆ’16x2 + 10x + m and g(x) = 2x – 1

Putting g(x) = 0 ⟹ 2x – 1 = 0 ⟹ x = 1/2


According to the factor theorem if g(x) is a factor of p(x) then p (1/2) = 0


p(1/2) = 8(1/2)4 + 4(1/2)3βˆ’16(1/2)2 + 10(1/2) + π‘š = 0


⟹




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