Question

2x^3+mx^2+11x+m+3 is exactly divisible by 2x-1. What is m?

Answer 1

Answer:

-7

Step-by-step explanation:

p(x)= 2x³+mx²+11x+m+3

∴2x-1=0

⇒2x=1

⇒x=1/2

p(1/2)=2(1/2)³+m(1/2)²+11(1/2)+m+3 = 0 (as it is exactly divisible, we'd write        

                                                                 p(1/2)=0)

⇒p(1/2)= 2*1/8+ m/4 +11/2 + m + 3 = 0

⇒p(1/2=  1/4+m/4+11/2+m= -3

⇒p(1/2)= m/4 + m= -3 -11/2 -1/4

⇒p(1/2) = m+4m/4 = -12/4 - 22/4 -1/4

⇒p(1/2) = 5m/4= -35/4

⇒p(1/2)= m = -35/4*4/5

∴m=-7

Therefore, m = -7

I hope it'll help you. Have  good day :)