-") are the factors of px + 5x+r, s...
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-") are the factors of px + 5x+r, show that p=r Q10 If both (x - 2) and (x - 12) are the factors of py

11th - 12th Class
Maths
Solution
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If ( (x-2) ) & ( (x-1 / 2) ) are facter of ( p x^{2}+5 x+r ) ( Rightarrow p(2)^{2}+5 times 27 gamma=0 ) ( Rightarrow 4 p+gamma=-10 ) ( pleft(frac{1}{2}right)^{2}+frac{5}{2}+gamma=0 ) ( Rightarrow frac{p}{4}+gamma=-5 / 2 ) Sub. 2 from ( frac{sin ^{2} p}{4}=frac{-sqrt{5}-1}{2} Rightarrow p=-2 ) ( 8 gamma=-2 ) ( Rightarrow p=gamma ) Hence proved
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