Math, asked by arulmozhivarman848, 3 months ago

Find a quadratic polynomial if the sum and product of the zero is -1/√2 and 1/√2​

Answers

Answered by Anonymous
5

Solution

Given:-

 \tt \implies \:  \alpha  +  \beta  =  \dfrac{ - 1}{ \sqrt{2} }

 \tt \implies \:  \alpha  \beta  =  \dfrac{1}{ \sqrt{2} }

The Expression of quadratic equation is

 \tt \implies \:  {x}^{2}  - (sum \: of \: the \: roots)x + (product \: of \: the \: roots) = 0

It's Mean

 \tt \implies \:  {x}^{2}  - ( \alpha  +  \beta )x +  \alpha  \beta  = 0

Now Put the Value

 \tt \implies \:  {x}^{2}   -  \bigg( \dfrac{ - 1}{ \sqrt{2} }  \bigg)x +  \dfrac{1}{ \sqrt{2} }  = 0

 \tt \implies \:  {x}^{2}    +   \dfrac{ 1}{ \sqrt{2} }  x +  \dfrac{1}{ \sqrt{2} }  = 0

Now Taking Lcm

 \tt \implies \dfrac{ \sqrt{2}  {x}^{2}  + x + 1}{ \sqrt{2} }  = 0

 \tt \implies \:  \sqrt{2}  {x}^{2}  + x + 1 = 0

The quadratic polynomial Equation is

 \tt \implies \:  \sqrt{2}  {x}^{2}  + x + 1 = 0

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