Question

Find the value of p, if (2x-1) is a factor of 2x^(3)+px^(2)+11x+p+3

Answer 1

Heya !!!



(2X-1) is a factor of the given Polynomial.



(2X -1) = 0


2X = 1



X = 1/2



P(X) = 2X³ + PX² + 11X + P + 3



P(1/2) = 0 because 1/2 is a zero of the given Polynomial.




P(1/2) = 0



2 × (1/2)³ + P × (1/2)² + 11 × 1/2 + P + 3 = 0



2 × 1/8 + P × 1/4 + 11/2 + P + 3 = 0


1/4 + P/4 + 11/2 + P + 3 = 0




1 + P + 22 + 4P + 12 / 4 = 0





4P + P + 1 + 22 + 12 = 0 × 4





5P + 35 = 0



5P = -35




P = -35/5



P = -7.


HOPE IT WILL HELP YOU....... :-)

Answer 2

Given that (2x - 1) is the Factor,

So, 2x - 1 = 0

x = 1/2

×××××××××××××××××××

Putting the value of x in given equation,


2x³ + px² + 11x + p + 3 = 0

2(1/2)³ + p(1/2)² + 11(1/2) + p + 3 = 0

2(1/8) + p(1/4) + 11/2 + p + 3 = 0

1/4 + p/4 + 11/2 + p + 3 = 0

p + p/4 = -3 - 1/4 - 11/2

(4p + p)/4 = (-12 - 1 -22)/4

5p = -35

p = -35/5

p = -7




I hope this will help you

(-: