Find all real zeros and state their multiplicities of each p

Find all real zeros (and state their multiplicities) of each polynomial function.

f(x) = 8x³ + 6x² - 27x

Solution

f(x) = 8x³ + 6x² - 27x

for zeroes

8x³ + 6x² - 27x=0

=>x( 8x² + 6x - 27)=0

=> x =0 ,  8x² + 6x - 27=0

=> x =0 ,  8x² + 6x = 27

=> x =0 , x² + (3_/4)x = (27_/8)

=> x =0 , x² + (3_/4)x + (3_/8)²= (27_/8)+ (3_/8)²

=> x =0 , (x + (3_/8))²= (27_/8)+ (9_/64)

=> x =0 , (x + (3_/8))²= (225_/64)

=> x =0 , (x + (3_/8))= (-15_/8) , (x + (3_/8))= (15_/8)

=> x =0 , x = (-18_/8) , x = (12_/8)

=> x =0 , x = (-9_/4) , x = (3_/2)

zeroes are x= (-9_/4) ,0 , (3_/2) with each having multiplicity 1