Question

Find a cubic polynimial whose zeros are 1,-2 and 3

Answer 1

Step-by-step explanation:

alpha+beta+gama = 1

-b/a =1

alpha(beta)+beta(gama)+gama(alpha)= -2

c/a= -2

(alpha)(beta)(gama)= 3

-d/a= 3

cubic polynomial form = ax³+bx²+cx+d

required cubic polynomial is x³+(-1x²)+(-2x)+(-3)

= x³-x²-2x-3

Answer 2

Answer: x³-2x²-5x+6

Step-by-step explanation:

Let p,q and r be the 3 roots

p+q+r = 1-2+3= 2

-b/a =-2

pq+qr+rp= -2-6+3=-5

c/a= -5

pqr= -6

-d/a= 6

cubic polynomial form = ax³+bx²+cx+d

                                     = x³+$\frac{-b}{a}$x²+$\frac{c}{a}$x+$\frac{-d}{a}$

required cubic polynomial is x³+(-2x²)+(-5x)+(6)

= x³-2x²-5x+6

This is the right answer. Hope it helps! Peace out✌