Question

Solve With Steps ......... Will be marked As BRAINLIEST

Answer 1

Answer:

a = 1   and  b = 4

Step-by-step explanation:

Given expression is 2x^3 - ax^2 - 8x + b. If ( 2x - 1 ) and ( x + 2 ) are its factors, its value must be 0 for x = 1/2 and for x = -2.

 For x = 1 / 2

⇒ 2(1/2)³ - a(1/2)² - 8(1/2) + b = 0

⇒ 2(1/8) - a(1/4) - 8(1/2) + b = 0

⇒ (1/4) - (a/4) - 4 + b = 0

⇒ ( 1 - a - 16 + 4b ) / 4 = 0

⇒ 4b - a - 15 = 0

⇒ 4b - a = 15

      For x = - 2

⇒ 2(-2)³ - a(-2)² - 8(-2) + b = 0

⇒ 2(-8) - a(4) - 8(-2) + b = 0

⇒ - 16 - 4a + 16 + b = 0

⇒ b - 4a = 0

⇒ 4a = b

    Hence,

   4b - a = 15

   4( 4a ) - a = 15

   16a - a = 15

   15a = 15

       a = 1

Hence, b = 4a = 4(1) = 4

Answer 2

Answer:

a=1, b=4

Step-by-step explanation:

by remainder theorem

2x-1=0

x=1/2 is a zero of the polynomial

x+2=0

x= -2 is a zero of the polynomial

if we put x=-2,1/2

polynomial will give same value i.e zero

for x = -2

2 x (-2)^3 - a x (-2)^2 - 8 x (-2) + b=0

-16 - 4a+16+b =0

b-4a =0

for x = 1/2

2 x (1/2)^3 - a x (1/2)^2 - 8 x (1/2) + b=0

1/4 - 1/4 a -4 + b =0

hence

1/4 - 1/4 a -4 + b = b -4a

15/4 a = 15/4

a=1

put value of a in equation

b-4a=0

b-4=0

b=4