Question

if two roots of x cube minus 3 x minus 2 equal then the third root is​

Answer 1

Answer:

Step-by-step explanation:

Given,a,b are distance roots of x  3 +3x  2  −1=0

⇒a  3  +3a  2  −1=0 and  b  3 +3b  

2 −1=0

let the third root be c

then c  3  +3c  2 −1=0

product of roots =  a −d

​ =  1 −(−1)

​=1 ⇒  abc=1  

c=  ab 1    

but c is root of x  3 +3x  2 −1=0 ⇒c  3  +3x  

2  −1=0 ⇒  (ab)  3 1 +  (ab)  2 3  −1=0

⇒  1+3ab−(ab)  3  =0

​ .....(1)

in equation (1)

(ab)  3 −3(ab)−1=0

⇒ab is root of x  3  −3x−1=0

∴(ab) is root of  

x  3  −3x−1=0

​