Question

6. If one root of the equation (k-1)2 - 10x + 3 = 0 is the reciprocal of the other then the value of k
7. If the sum and product of the zeroes of a quadratic polynomial are 3 and -10 respectively, find the quadra
polynomial.​

Answer 1

$\huge { \green{Q.6 }}$

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ɢɪᴠᴇɴ :-

• If one root of the equation (k-1)² - 10x + 3 = 0 is the reciprocal of the other

ᴛᴏ ғɪɴᴅ :-

• Find the value of k

ʀᴇϙᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ :-

$➝ \: \: (k - 1) ^{2} - 10x + 3 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \: \:ᴏɴᴇ \: \: ʀᴏᴏᴛ \: \: ɪs \: \: ' a ' \: \: ᴏᴛʜᴇʀ \: \: ɪs \: \:' \frac{1}{a}' \\ \\ ➝ \: \:ᴡᴇ \: \: ᴋɴᴏᴡ \: \: ᴛʜᴀᴛ \: \: \: \: \: \: \: \: \\ \\ ➝ \: \:( ᴍᴜʟᴛɪᴘʟʏ \: \: ᴏғ\: \: ᴛᴡᴏ\: \: ᴢᴇʀᴏs \: \:= ᴄ/ᴀ\: \: ᴛʜᴀᴛ's \: \:ᴡʜʏ ) \\ \\ ➝ \: \:(a \times \frac{1}{a} ) = \frac{ᴄ}{ᴀ} \: = \frac{3}{(k - 1)} \: \: \:\: \: \: \: \: \: \: \\ \\ ➝ \: \:1 = \frac{3}{k - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \: \:k - 1 = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \: \:k = 3 + 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➝ \: \:k = 4\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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I hope it helps you ❤️✔️✔️

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