Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively √(2) \: \: \: and \ \frac{1 }3 ​

Question

Find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively


`√(2) \: \: \: and \ \frac{1 }3`
​

Answer 1

`\alpha + \beta = √(2)`

`\alpha \beta = (1)/(3)`

The quadratic equation is given by

`y = {x}^(2) - ( \alpha + \beta )x + \alpha \beta`

`y = {x}^(2) -x √(2) + (1)/(3)`