Find the quadratic polynomial ,the sum …
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Rashmi Bajpayee 6 years, 8 months ago
Let the roots of quadratic equation be {tex}\alpha{/tex} and {tex}\beta{/tex}.
Then Sum of roots = {tex}\alpha{/tex} + {tex}\beta{/tex} = {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} = {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}
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