Question

Find a quadratic polynomial the sum and product of whose zeroes are - 3 and - 2 respectively

Answer 1

Step-by-step explanation:

given,

α+β = -3.

αβ = -2.

quadratic formula is

x^2-x(α+β)+(αβ)=0.

x^2-x(-3)+(-2)=0.

x^2+3x-2=0.

therefore x^2+3x-2=0 is the quadratic equations whose sum is -3 .

and product is-2.

Answer 2

Answer:  x² + 3x - 2

Step-by-step explanation:

Let the zeroes of polynomial be α and β.

Now,

Sum of zeroes = -3

α + β = -3

Product of zeroes  = -2

αβ = -2

We know that,

A quadratic polynomial having zeroes α and β is,

x² - (α + β)x + αβ

x² -(-3)x + (-2)

x² + 3x - 2

Hence, Polynomial is x² + 3x - 2