Question

if both X - 2 and x minus one upon two factors of P X square + 5 x + r so that p=r

Answer 1

THE GIVEN POLYNOMIAL IS

q(x)=px²+5x+r ............1

if x-2 is the factor of q(x) then 9(2)=0

⇒ p(2)²+5×2+r=0

⇒ 4p+r+10=0 .............2

if x-1/2 is the factor of q(x) then q(1/2)=0

⇒p(1/2)²+5×1/2+r=0

⇒p/4+5/2+r=0

⇒p+4r+10=0 ..............3

subtracting 3 from 2 ;

⇒ 4p+r+10-(p+4r+10)=0

⇒3p-3r=0

⇒3p=3r

⇒p=r.

hence proved.