THE BESTSELLING book Roots , Alex Haley's historical reconstruction of how his family came from relative freedom in Africa to certain slavery in America, and then from slavery to relative freedom today, has spurred many black Americans to think about and search out their own roots.

A few years ago most blacks were either ashamed or afraid to tell the story of their struggle for survival against enormous odds. Their reticence derived in part from the frequent ugliness of their stories.

On these four pages are the true stories of eight Washingtonians who not only survived exploitation but went on to achieve prominence in a world dominated by whites.

Peggy Cooper, 29, is special assistant to the president of Post-Newsweek Stations as well as a programming executive and documentary producer of WTOP-TV. She is also a lawyer and a member of the D. C. Bar.

On her mother's side of the family, everyone is from Lafayette, Louisiana, in the heart of Catholic Creole country. Peggy's great-great-grandmother, Artemis Mouton, was a midwife and the daughter of a slave. Her daughter Julie, Peggy Cooper's great-grandmother, used to tell her stories about how the Ku Klux Klan - very active in Lafayette - used to hunt down black children and dump them in the Mississippi River. Julie remembered that her relatives would hide her in the armoire when the Klan came.

Julie grew up to be the first black woman in town to live openly with a white man. Paul Mouton, the son of the governor of Louisiana, was according to Peggy Cooper, defintely considered the failure of his family, but he was not disowned for living with Julie in her house.

In later life, when Pual Mouton became gravely ill, his family took him back to the main house and they allowed Julie to come visit - but only through the back door. It is said that at the cemetery in Lafayette he is buried between his white wife and his black wife.

Julie was a midwife like her mother. She was also the first black in Lafayette to have electricity and indoor plumbing.

Julie and Paul had five children, Peggy's grandmother Agnes among them. She married Clarence Mouton - no relation. Mouton was a common name in Lafayette. Agnes, who was self-educated, managed to send all four of her girls through black Catholic schools and to college. Peggy's mother went to Hampton Institute in Virginia where she met and married Algernon Johnson Cooper.

Clarence Mouton was part Indian as is Peggy Cooper's father. The paternal side of her history goes back to the Seminole Indians in Florida. Her great-great-great-grandfather was Chief Osceola. His daughter, half black and half Indian, married the son of an English barrelmaker and his Irish wife. They had a son (one-quarter black, one-quarter Indian, one-quarter English, one-quarter Irish) named Osceola Osceola Cooper, who in turn had a son by the same name (Peggy's grandfather). He somehow ended up in Evansville, Indiana, and went to Fisk University where he met and married Peggy's grandmother, a native of Mobile.

After their graduation from Fisk in 1903, the grandparents settled in Mobile. Peggy Cooper's father, Algernon, was born there as were Peggy and her five brothers and sisters.