Question

If a, ß are roots of ax? + bx + c = 0, then :
ax^2 +(2a+b)x +(a+b+c)
the following roots of the following equation is
​

Answer 1

• ᴛʜᴇsᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴅᴏ ɴᴏᴛ ʜᴀᴠᴇ ʀᴇᴀʟ ʀᴏᴏᴛs ᴛʜᴇɴ ɪᴛ ɪᴍᴘʟɪᴇs ᴛʜᴀᴛ ᴛʜᴇ ɢʀᴀᴘʜ ᴏғ ᴛʜɪs ᴇϙᴜᴀᴛɪᴏɴ ᴅᴏ ɴᴏᴛ ᴛᴏᴜᴄʜ x ᴀxɪs.

• ғᴜʀᴛʜᴇʀ
• ғ(1)=ᴀ+ʙ+ᴄ<0

• ᴛʜɪs ɪᴍᴘʟɪᴇs ᴛʜᴀᴛ ᴛʜᴇ ɢʀᴀᴘʜ ᴏғ ᴛʜᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴡɪʟʟ ᴏᴘᴇɴ ᴅᴏᴡɴᴡᴀʀᴅs .

• sᴏ ᴀ<0
• sɪɴᴄᴇ ᴛʜᴇ ᴇϙᴜᴀᴛɪᴏɴ ʜᴀs ɴᴏ ʀᴇᴀʟ ʀᴏᴏᴛs ᴅɪsᴄʀɪᴍɪɴᴀɴᴛ ɪs ʟᴇss ᴛʜᴀɴ 0.

ᴀʟsᴏ ᴄ<0 ʙᴇᴄᴀᴜsᴇ ᴏғ ᴛʜᴇ ғᴀᴄᴛ ᴛʜᴀᴛ ʙ^2-4ᴀᴄ<0

Answer 2

Answer:

THESE EQUATION DO NOT HAVE REAL

ROOTS THEN IT IMPLIES THAT THE

GRAPH OF THIS EQUATION DO NOT

TOUCHX AXIS.

FURTHER

F(1)=A+B+C<0

THIS IMPLIES THAT THE GRAPH OF THE

EQUATION WILL OPEN DOWNWARDS

sO A<0

SINCE THE EQUATION HAS NO REAL

ROOTS DISCRIMINANT Is LESS THAN O.

ALSO C<O BECAUSE OF THE FACT THAT

B2-4AC<0