Question

if sum of the squares of zeros of quadratic polynomial f x is equal to x square - 8 x + K is 40 then find the value of k

Answer 1

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ᴘ (x)= x^2-8x+ᴋ
ᴘ (x)=ᴀx^2+ʙx+ᴄ
( ɪɴ ᴛʜɪs ғᴏʀᴍ)

ʟᴇᴛ ᴛʜᴇ ᴢᴇʀᴏᴇs ʙᴇ 'ᴀ' ᴀɴᴅ 'ʙ'

ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ 
=> ᴀ^2+ʙ^2=40
=> (ᴀ+ʙ)^2 - 2ᴀʙ = 40 __1

sᴜᴍ ᴏғ ᴢᴇʀᴏᴇs
=> ᴀ+ʙ = -ʙ/ᴀ = -(-8)/1 = 8

ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴢᴇʀᴏᴇs
=> ᴀ*ʙ = ᴄ/ᴀ  = ᴋ

sᴜʙsᴛɪᴛᴜᴛᴇ ᴛʜᴇsᴇ ᴠᴀʟᴜᴇs ɪɴ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ1 ᴡᴇ ɢᴇᴛ
=> 8^2 - 2ᴋ = 40
=> 64 - 2ᴋ = 40
=> 2ᴋ = 24
=> ᴋ = 12

ᴛʜᴇʀᴇғᴏʀᴇ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴋ ɪs 12

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