Find the quadratic polynomial ,the sum of whose root is √2 and their

1.	Find the quadratic polynomial ,the sum of whose root is √2 and their product is 1/3\xa0
Answer» Ans.Given : Sum of roots =\xa0{tex}\\sqrt 2{/tex}Product of roots =\xa0{tex}{1\\over 3}{/tex}We know,\xa0Sum of roots =\xa0{tex}-b\\over a{/tex}=>\xa0{tex}{\\sqrt 2\\over 1 } = {-b\\over a}{/tex}=>\xa0{tex}{3\\times \\sqrt 2\\over 1\\times 3 } = {-b\\over a}{/tex}=>\xa0{tex}{3 \\sqrt 2\\over 3 } = {-b\\over a}{/tex}On comparing,we get, a = 3 and b =\xa0{tex}-3\\sqrt 2{/tex}Also,\xa0Products of the root =\xa0{tex}c\\over a{/tex}=>\xa0{tex}{1\\over 3} = {c\\over a}{/tex}on comparing a = 3 and c = 1So required polynomial :\xa0{tex}3x^2 -3\\sqrt 2x+1{/tex}

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