Question

po ( f(x)=p x^{2}+5 x+gamma )
( because x-2 ) and ( x^{prime}-frac{1}{2} ) are factors of ( f(x) )
( Rightarrow x=2 ) aud ( x=frac{1}{2} ) satisfy the ( f(x) )
( Rightarrow f(2)=0 quad ) & ( quad fleft(frac{1}{2}right)=0 )
( Rightarrow quad 4 p+10+gamma=0 )
( & frac{b}{4}+frac{5}{2}+r=0 )
Seletractivg ( Rightarrow 4 p+r+10=0 ) & ( p+10+4 r=0 )
Subtractive both fle equations,
[
(4 p+gamma+10)-(p+10+4 r)=0-0
]
( Rightarrow quad 3 p-3 gamma=0 )
( Rightarrow quad 3 b=3 gamma )
( Rightarrow quad sqrt{p=gamma} )
Ferce, proved

# 17. If(x-2) and (x - 2) are the factors of the polynomial px?+5x+r, prove that p = 1. ht

Solution