Question

write a quadratic polynomial if the sum and product of its zeros are √2 and 1/3.​

Answer 1

Answer:

3x^2 - 3√2 x + 1

Step-by-step explanation:

given:          sum of zeros = √2                  product of zeros= 1/3

                   alpha + beta = √2                   alpha*beta= 1/3

quadratic polynomial = x^2 - (alpha + beta)x +(alpha * beta)

                                   = x^2 - √2 x + 1/3

                                   = (3x^2 - 3√2 x + 1) / 3

therefore, 3x^2 - 3√2 x + 1 is the required quadratic polynomial.