Question

write a quadratic polynomial whose zeros are (root 2 + 1) and (root 2 - 1) ​

Answer 1

Step-by-step explanation:

1st root = √2 + 1

2nd root = √2 - 1

Sum of roots, S = √2 + 1+√2 - 1 = 2√2

Product of roots, P =(√2 - 1)(√2 +1)= 2-1=1

Now quad polynomial=

${x}^{2} - sx + p$

$x {}^{2} - 2\sqrt{2} x \: + 1$

Answer 2

Given roots are $\sqrt{2}+1 , \sqrt{2}-1$

We need to find the quadratic expression

We have the general form of a quadratic expression $x^2+(a+b)x+ab$, where a and b are the roots of this quadratic equation.

The Sum of roots is

$\sqrt{2}+1+\sqrt{2}-1\\=2\sqrt{2}$

Product of roots is

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

Therefore, the required quadratic expression is $x^2+2\sqrt{2}x+1$

To learn more about quadratic equations from the given link

https://brainly.in/question/24270338

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