Question

FIND THE QUADRATIC POLYNOMIAL THE SUM OF WHOSE ROOTS IS √2 AND THERE PRODUCT IS 1/3

Answer 1

Heya!
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◾Given that ,
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Sum of Zeroes => √2

Product of Zeroes => 1/3

To find : p ( x )

◾Here we can use the formula ,

p ( x ) = x² - sx + p

=> x² - √2x + 1/3 = 0

= Taking LCM,

LCM = 3


The Above equAtion becomes ,


3x² - 3√2 x + 1


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Answer 2

✤Qᴜᴇꜱᴛɪᴏɴ :-

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Find The QUADRATIC POLYNOMIAL the sum of whose roots is √2 and there product is 1/3.

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✤ᴡʜᴀᴛ ᴛᴏ ᴅᴏ :-

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• Find the polynomial

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✤ɢɪᴠᴇɴ

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• sum of roots = √2
• product of roots = 1/3

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✤ꜱᴏʟᴜᴛɪᴏɴ :-

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We know that,

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$\bf \implies {x}^{2} - ( \alpha + \beta)x + \alpha \beta$

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Putting the values

$\bf \implies {x}^{2} - \sqrt{2} x + \frac{1}{3}$

Taking the LCM

$\bf \implies \frac{3 {x}^{2} - 3 \sqrt{2}x + 1 }{3} = 0$

Multiply it by the constant term k

$\bf \implies k( \frac{3 {x}^{2} - 3 \sqrt{2}x + 1 }{3} ) = 0$

Let k = 3

$\bf \implies 3( \frac{3 {x}^{2} - 3 \sqrt{2}x + 1 }{3} ) = 0$

$\bf \implies {\cancel3}( \frac{3 {x}^{2} - 3 \sqrt{2}x + 1 }{ \cancel3} ) = 0$

So, the required polynomial is :-

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$\bf \implies 3 {x}^{2} - 3 \sqrt{2} x + 1 = 0$