Question

If α+β=-3and α*β=2,form a quadratic polynomial where α and β are the zeroes of the polynomial?​

Answer 1

Answer:

X^2  + 3 X + 2=0

Step-by-step explanation:

a quad equation can also be written as

X^2  - (SOR)x + (POR)=0

SOR = sum of roots = α+β = -3

POR = Product of roots = α*β = 2

so Equation is

X^2  + 3 X + 2=0

Answer 2

$\sf\huge\underline{Answer:}$

Given α+β=-3 and α*β=2 where α and β are the zeroes of the polynomial.

If α and β are zeroes of a polynomial, then the polynomial would be :

$k[ {x}^{2} - ( \alpha + \beta )x + \alpha \beta ]$

$k[ {x}^{2} - ( - 3)x + 2 ]$

$k[ {x}^{2} + 3x + 2 ]$

Here k might be any number, if we consider k = 1

Quadratic polynomial will be ${x}^{2} + 3x + 2$

Have a good evening!