Question

Express quadratic polynomial with 1+√2,1-√2 are zeroes​

Answer 1

Answer:

$\large\boxed{\sf{{x}^{2}-2x-1}}$

Explanation:

Given that the zeroes of a quadratic polynomial are,

• 1 + √2
• 1 - √2

To find the quadratic polynomial.

First of all find the sum of zeroes

=> Sum of zeroes = (1+√2)+(1-√2)

=> Sum of zeroes = 2

Now, find the product of zeroes.

=> Product of zeroes = (1+√2)(1-√2)

=> Product of zeroes = (1)^2 - (√2)^2

=> Product of zeroes = 1 - 2

=> Product of zeroes = -1

Now, we know that, a quadratic Polynomial can be written as,

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

Therefore, we will get,

= x^2 - 2x - 1

Hence, the required quadratic polynomial is ${x}^{2}-2x-1$.