Question

If alpha and beta are the zeros of a quadratic polynomial such that alpha+beta=48 and alpha-beta=16, find a quadratic polynomial having alpha and beta as its zeros.

Answer 1

Alpha +beta = 24 .......(1) . Alpha-beta=8......(2). adding (1) and (2) we get Alpha = 16. so beta=8. Quadratic polynomial= K[ x^2-(alpha+ beta)x +alpha×beta]=K[x^2-24x+192] where k is arbitrary constant. we can take k =1.


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Answer 2

ʜᴇʏᴀ!!

ʜᴇʀᴇ's ʏᴏᴜʀ ᴀɴsᴡᴇʀ

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ɢɪᴠᴇɴ , ᴀʟᴘʜᴀ + ʙᴇᴛᴀ = 48 ---------- ( ɪ )

ᴀɴᴅ , ᴀʟᴘʜᴀ - ʙᴇᴛᴀ = 16 ----------- ( ɪɪ )

• ᴛᴏ ғɪɴᴅ ᴛʜᴇ ϙᴜᴀᴅʀᴀᴛɪᴄ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴡᴇ ɴᴇᴇᴅ ᴛᴏ ғɪɴᴅ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴀʟᴘʜᴀ ᴀɴᴅ ʙᴇᴛᴀ ғᴀsᴛ.

ɴᴏᴡ , ᴇϙᴜᴀᴛɪᴏɴ ( ɪ ) + ( ɪɪ ) 

ᴀʟᴘʜᴀ + ʙᴇᴛᴀ + ᴀʟᴘʜᴀ - ʙᴇᴛᴀ = 48 + 16

ᴏʀ , 2 ᴀʟᴘʜᴀ = 64

ᴏʀ , ᴀʟᴘʜᴀ = 64 / 2

ᴏʀ , ᴀʟᴘʜᴀ = 32

ɴᴏᴡ , ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴀʟᴘʜᴀ ɪɴ ᴇϙᴜᴀᴛɪᴏɴ-- ( ɪ )

ᴀʟᴘʜᴀ + ʙᴇᴛᴀ = 48

ᴏʀ , 32 + ʙᴇᴛᴀ = 48

ᴏʀ , ʙᴇᴛᴀ = 48 - 32

ᴏʀ , ʙᴇᴛᴀ = 16

sᴏ , ᴀʟᴘʜᴀ = 32 ᴀɴᴅ ʙᴇᴛᴀ = 16

• ɴᴏᴡ ɪғ ᴛʜᴇ ᴢᴇʀᴏs ᴏғ ᴛʜᴇ ϙᴜᴀᴅʀᴀᴛɪᴄ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴀʀᴇ ᴀʟᴘʜᴀ ᴀɴᴅ ʙᴇᴛᴀ ᴛʜᴇɴ ᴛʜᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴡɪʟʟ ʙᴇ :-

x^2 + ( ᴀʟᴘʜᴀ + ʙᴇᴛᴀ ) x + ᴀʟᴘʜᴀ × ʙᴇᴛᴀ = 0

= x^2 + ( 32 + 16 ) x + 32 × 16 = 0

= x^2 + 48 x + 512 = 0

sᴏ , ᴛʜᴇ ϙᴜᴀᴅʀᴀᴛɪᴄ ᴘᴏʟʏɴᴏᴍɪᴀʟ ɪs x^2 + 48x + 512 = 0

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ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ ᴅᴇᴀʀ! :)

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