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| 1. |
Find the quadratic polynomial ,the sum of whose roots is √2 and their product is 1/3 |
| Answer» Let the roots of quadratic equation be {tex}\\alpha{/tex}\xa0and {tex}\\beta{/tex}.Then Sum of roots = {tex}\\alpha{/tex}\xa0+ {tex}\\beta{/tex}\xa0= {tex}\\sqrt 2 {/tex}=> {tex}{-b \\over a} = {{\\sqrt 2 } \\over 1}{/tex}=> {tex}{-b \\over a} = {{\\sqrt 2 } \\over 1} \\times {3 \\over 3}{/tex} => {tex}{-b \\over a} = {{3\\sqrt 2 } \\over 3}{/tex} ..............(i)And, Product of roots = {tex}\\alpha{/tex}.{tex}\\beta{/tex}\xa0= {tex}{1 \\over 3}{/tex}=> {tex}{c \\over a} = {1 \\over 3}{/tex} ................(ii)On comparing both the equations, we have{tex}a = 3,b = - 3\\sqrt 2 ,c = 1{/tex}Putting these values in the general quadratic equaiton {tex}a{x^2} + bx + c = 0{/tex}, we get{tex}3{x^2} - 3\\sqrt 2 x + 1 = 0{/tex} | |