Question

if (X= 2) and x-1/2 are factors of px²+2x +r . show that p=r​

Answer 1

Answer:

p=r

Step-by-step explanation:

according to remainder theorem

if p(x)/g(x)=(px²+2x+r/ x-2)

then remainder is p(2).

so p2²+4+r=0 [.: 0 because x=2 ]

4p+4+r=0

4p+r=-4

Now since x-1/2 is a factor hence the remainder is 0

so x=1/2

p(1/2)=(p/4)+1+r=0

(p+4+4r)/4=0

p+4+4r=0

4r+p= -4

4r+p=-4=4p+r

4r+p=4p+r

After canceling p and r from both sides we get

3p=3r

.:p=r