Question

find a quadratic polynomial whose zeros are 1 and -3 verify the relation between coefficient and zeros of polynomial .

Answer 1

zeros are 1 and -3
let
$1 = \alpha \\ 2 = \beta$
sum of zeros
$\alpha + \beta$
=1+(-3)
=1-3
= -2

product of zeros
$\alpha \beta$
= 1(-3)
=-3
Quardratic polynomial is
${x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) \\ {x}^{2} - ( - 2)x \: + ( - 3) \\ {x}^{2} + 2x - 3$

ax^2+bx+c=0
a=1
b=2
c=-3

verifiction
alpha +beta=-b/a
-2=-2/1
-2=-2
aplha*beta=c/a
-3=-3/1
-3=-3