Question

Find the value of a if 2x-3 is factor of 2x⁴-x³-3x²+4x-a *​

Answer 1

Answer:

a = 3

Step-by-step explanation:

p ( x ) = 2x ^ 4 - x ^ 3 - 3x ^ 2 - 2x + a

if  2x - 3 is a factor,

2x - 3 = 0

=> 2x = 3

=> x = 3 / 2

p ( 3 / 2 ) = 2 * ( 3 / 2 ) ^ 4 - ( 3 / 2 ) ^ 3 - 3 * ( 3 / 2 ) ^ 2 - 2 * 3 / 2 + a

= 2 * 81 / 16 - 27 / 8 - 3 * 9 / 4 - 3 + a

= 81 / 8 - 27 / 8 - 27 / 4 - 3 + a

= 54 / 8 - 27 / 4 - 3 + a

= 27 / 4 - 27 / 4 - 3 + a

= - 3 + a

=> - 3 + a = 0

=> a = 3