Question

Quadratic polynomial x2 -3x -2 has zeroes as α and β.Now form a quadratic polynomial whose zeroes are 1/ (2 α + β) and 1/ (2 β+ α)

Answer 1

To form a quadratic polynomial with given zeroes, find the sum and product of the zeroes and then use those values to create the quadratic equation.

Step-by-step explanation:

To form a quadratic polynomial with zeroes 1/(2α+β) and 1/(2β+α), we need to find the sum and product of the zeroes and then use those values to create the quadratic equation.

Given that the zeroes of the quadratic polynomial x^2-3x-2 are α and β, we have:

Sum of zeroes (α + β) = -(-3) = 3

Product of zeroes (α * β) = -2

Now substitute the values of α + β and α * β into the quadratic equation (x^2-(α + β)x+α * β)=0 to get the desired polynomial.