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Find the quadratic polynomial ,the sum …

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Find the quadratic polynomial ,the sum of whose roots is √2 and their product is 1/3

  • 1 answers

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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