Question

what is the quadratic polynomial whose sum of zeros is 5/3 and the product of zeros is 1

Answer 1

Heya !



Sum of zeroes = 5/3


and,


Product of zeroes = 1



Therefore,




Quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes




=> X² - (5/3)X + 1


=> X² - 5X/3 + 1



=> 3X² - 5X + 3



Hence,


Required quadratic polynomial = 3X² - 5X + 3

Answer 2

Hey dear!!!

___________________________

==>>> Solution

Let the zeroes of the unknown quadratic polynomial be α and β .

According to the given data we have,

Sum of zeroes (α + β) = 5/3

and

Product of zeroes (αβ) = 1

We have to find the required quadratic polynomial .

We know that,

=> x² - (sum of zeroes(α +β)x + (product of zeroes(αβ)

Now,put the obtained values we get,

=> x² - (5/3)x + 1

=> x² - 5x/3 + 1

Now multiply the whole equation by 3 we get,

=> 3*x² - 3*5x/3 + 3*1

3 and another 3 which have in the denominator got cancelled .

Hence,

=> 3x² - 5x + 3

∴ The required quadratic polynomial is 3x² - 5x + 3

Thanks !!!!

✴✴✴✴✴✴ R.N.S✴✴✴✴✴✴✴✴