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## Answers

*x-2=0*

x=2 (factor of the polynomial)

x+1/2=0

x=-1/2 (factor of the polynomial)x=2 (factor of the polynomial)

x+1/2=0

x=-1/2 (factor of the polynomial)

*x-2 as a factor,*

*∴*

*px^2+4(2)+r= 0*

*⇒4p+8+r=0 ----------------------------(1)*

*now, x=+1/2 as a factor*

*p(-1/2)^2+4( -1/2)+r=0.*⇒

*1/4p-4/2=0 --------------------------(2)*

*from the equation (1) and (2)*

*4p+8+r=1/4p-4/2+r=0*

*⇒4p-1/4p=-4/2-8+r-r*

*⇒(16p-1p)/4=-20/2*

*⇒15p/4=-10*

*⇒15p=-10*4*

*⇒15p=40*

*⇒p=40/15*

*⇒p=8/3*

*∴in the equation 3p+16=3r*

*⇒ 3(8/3)+16=3r*

*⇒ 8+16=3r*

*⇒24=3r*

*⇒24/3=r*

*⇒8=r*

*∴by putting the value of p and r in the given equation ,*

*we get,*

*3p+16=3r.*

*3(8/3)+16=3(8)*

*8+16=24*

*24=24*

*∴R.H.S=L.H.S*

*hence proved.**i hope that it will help u...............*