Question

13. Find the quadratic polynomial whose sum and product of zerors are \|2 +1, 1/ \|2+1​

Answer 1

Answer:

$\large\boxed{\sf{ {x}^{2} - ( \sqrt{2} + 1)x + \dfrac{1}{ \sqrt{2} + 1 } }}$

Step-by-step explanation:

Given that,

There's a quadratic polynomial such that

Sum of roots = √2+1

Product of roots = 1/(√2+1)

Now, to find the quadratic polynomial

We know that, a quadratic polynomial is given by

= x^2-(sum of roots)x + (product of roots)

Therefore, we will get,

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

Hence, the required quadratic polynomial is $\bold{ {x}^{2} - ( \sqrt{2} + 1)x + \dfrac{1}{ \sqrt{2} + 1 } }$