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

11th - 12th Class
Maths
Solution
120
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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
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