Question

If a and B are the zeroes of the quadratic polynomial 6x2 - 37x + 6, then find the value of 1/α+1/β

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the value of 1/α+1/β

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

α and β are zeroes of quadratic polynomial 6x² - 37x + 6

• Polynomial = 6x² - 37x + 6
• a = 6
• b = -37
• c = 6

→ Sum of zeroes = -b/a

→ α + β = -(-37)/6

→ α + β = 37/6 ....2)

→ Product of zeroes = c/a

→ αβ = 6/6

→ αβ = 1 ......1)

Now, Finding value of 1/α+1/β

→ 1/α+1/β = (β + α)/αβ

▶ Putting values of α + β and αβ from 1) and 2)

→ 1/α+1/β = 37/6/1

→ 1/α+1/β = 37/6

Hence,

Value of 1/α+1/β = 37/6.

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Answer 2

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$\huge\bf\underline{SoutiOn \: : \: - }$

★ Α ᴀɴᴅ Β ᴀʀᴇ ᴢᴇʀᴏᴇꜱ ᴏꜰ Qᴜᴀᴅʀᴀᴛɪᴄ ᴘᴏʟʏɴᴏᴍɪᴀʟ

6x² - 37x + 6ᴘᴏʟʏɴᴏᴍɪᴀʟ

= 6x² - 37x + 6

• ᴀ = 6
• ʙ = -37
• ᴄ = 6

→ ꜱᴜᴍ ᴏꜰ ᴢᴇʀᴏᴇꜱ = -ʙ/ᴀ

→ Α + β = -(-37)/6

→ Α + β = 37/6 ....2)

→ ᴘʀᴏᴅᴜᴄᴛ ᴏꜰ ᴢᴇʀᴏᴇꜱ = ᴄ/ᴀ

→ Αβ = 6/6

→ Αβ = 1 ......1)

★ ɴᴏᴡ, ꜰɪɴᴅɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ 1/α+1/β

→ 1/α+1/β = (β + α)/αβ

★ Putting values of α + β and αβ from 1) and 2)

→ 1/α+1/β = 37/6/1

→ 1/α+1/β = 37/6

★ ʜᴇɴᴄᴇ, ᴠᴀʟᴜᴇ ᴏꜰ 1/α+1/β = 37/6.

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