Do we have to file married filing Jointly to get the EIC?

If you are legally married and have lived with your spouse at any time during the last six months of the year then you can only file a tax return as either Married Filing Jointly or Married Filing Separately.

If you choose file as MFS you are not eligible to claim EIC.

See this TurboTax support FAQ for filing jointly versus separately - https://ttlc.intuit.com/community/married/help/is-it-better-for-a-married-couple-to-file-jointly-or-separately/01/25590

good question  TC memo 2016-200 said MFS was ok but the IRS will not acquiesce with this decision. it points to IRC sec 32(d).   i think the IRS is right

there are other rules to qualify

if your interested, here's the link to the code section

https://www.law.cornell.edu/uscode/text/26/32

Q.  Do we have to file married filing Jointly to get the EIC?

A.  Simple answer: yes, if you are married.  See the other replies for details. See the answer to your second question for an exception.

Q. Can I file head of household (HoH) with 3 dependent's, and not The EIC ?

A . A legally married person can only file as HoH if they lived apart from their spouse for the entire lat half of the year (July 2- Dec 31). If you qualify for HoH, you also qualify for EIC.