if both X - 2 and x minus one upon two factors of P X square + 5 x + r so that p=r
Answers
Answered by
10
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.
Similar questions