Question

11 Find
find the value of m so that 2x-1 be a factor of 8x^4+4x^3-16x^2+10x+m
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Answer 1

Answer:

- 2

Step-by-step explanation:

Given :

p ( x ) =  8 x⁴ + 4 x³ - 16 x² + 10 x + m

Also 2 x - 1 is factor of p ( x ) :

Since ' 2 x - 1 ' is factor of p ( x ) remainder should be zero!

= > 2 x - 1 = 0

= > x = 1 / 2

Putting value of x in p ( x ) we get :

p ( 1 / 2 ) = 8 ( 1 / 2 )⁴ + 4 ( 1 / 2 )³ - 16 ( 1 / 2 )² + 10 ( 1 / 2 ) + m = 0

= > 8 / 16 + 4 / 8 - 16 / 4 + 10 / 2 + m = 0

= > 1 / 2 + 1 / 2 - 4 + 5 + m = 0

= >  1 + 1 + m = 0

= > 2 + m = 0

= > m = - 2

Hence we get required answer!