Question

Write a quadratic polynomial the sum and product of whose zeros are 3 and minus 2

Answer 1

In the attachment I have answered this problem.

Concept:

X^2 - (Sum of zeros) X + (Product of zeros)

See the attachment for detailed solution.

Answer 2

Solution :-

Here is the method to form a polynomial with the given zeros.

Let the zeros of a quadratic polynomial be α and β

x = α x = β

x - α = 0 x - β = 0

So, the required polynomial is

(x - α) (x - β)

i.e. x² - (α + β)x + αβ

⇒ x² - (Sum of the zeros)x + (Product of the zeros)

Quadratic polynomial with sum and product of whose zeros are 3 and - 2

Sum of the zeros = - 2 + 3 = 1

Product of the zeros = - 2 × 3 = - 6

Hence, the quadratic polynomial formed

x² - x - 6

Answer.

Answer 3

Solution :-

Here is the method to form a polynomial with the given zeros.

Let the zeros of a quadratic polynomial be α and β

x = α x = β

x - α = 0 x - β = 0

So, the required polynomial is

(x - α) (x - β)

i.e. x² - (α + β)x + αβ

⇒ x² - (Sum of the zeros)x + (Product of the zeros)

Quadratic polynomial with sum and product of whose zeros are 3 and - 2

Sum of the zeros = - 2 + 3 = 1

Product of the zeros = - 2 × 3 = - 6

Hence, the quadratic polynomial formed

x² - x - 6

Answer.