Question

Find a quadratic polynomial whose sum and products are -1 and 2

Answer 1

Answer:

The required quadratic polynomial is

$\bf{x^2+x+2}$

Step-by-step explanation:

$\text{Concept used}$

$\text{The quadratic polynomial having}\:\alpha\text{and}\beta\:\text{as roots is}\:x^2-(\alpha+\beta)x+\alpha\beta$

$\text{Given:}$

$\alpha+\beta=-1$

$\alpha\beta=2$

$\text{The required quadratic polynomial is}\:x^2-(\alpha+\beta)x+\alpha\beta$

$\implies\:x^2-(-1)x+2$

$\implies\:x^2+x+2$