Question

Find the Quadratic polynomial whose sum and product are root 2+1 and 1/root 2+1

Answer 1

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Answer 2

The quadratic polynomial is $(\sqrt{2} +1 )x^{2} -(\sqrt{2}+1 )^{2} x+1=0$.

Step-by-step explanation:

Given:

Sum and product  of roots are $\sqrt{2} +1$ and $\frac{1}{\sqrt{2} +1}$.

To Find:

The Quadratic polynomial.

Solution:

The General form of a quadratic polynomial whose Sum of roots and products of roots are given $x^{2} -(Sum\ of\ roots)x+(Product\ of\ roots)=0$.

As given-sum and product  of roots are $\sqrt{2} +1$ and $\frac{1}{\sqrt{2} +1}$.

The quadratic polynomial        

$x^{2} -(\sqrt{2} +1)x+(\frac{1}{\sqrt{2} +1} )=0$

$(\sqrt{2} +1 )x^{2} -(\sqrt{2}+1 )^{2} x+1=0$

Thus, the quadratic polynomial is $(\sqrt{2} +1 )x^{2} -(\sqrt{2}+1 )^{2} x+1=0$.

PROJECT CODE#SPJ2