Question

Find a quadratic polynomial whose zeroes are 3+ V5 and
$3 - \sqrt{5 }$
​

Answer 1

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✪QUESTION✪:-

Find a quadratic polynomial whose zeroes are $3 + \sqrt{5 }$ and

$3 - \sqrt{5 }$

✪ANSWER✪:-

➥Zeros of the polynomial are

• $3 + \sqrt{5 }$
• $3 - \sqrt{5 }$

➥SUM OF THE ZEROS

➥ $3 + \sqrt{5 }$ +$3 - \sqrt{5 }$

➥$6$

➥PRODUCT OF ZEROS

➥$(3 + \sqrt{5} )(3 - \sqrt{5} )$

It is in the form of

$( {a}^{2} - {b}^{2} ) = (a + b)(a - b)$

so,

➥${(3)}^{2} - {( \sqrt{5)} }^{2}$

➥$9 - 5$

➥$4$

QUADRATIC POLYNOMIAL :

➠${x}^{2} - (sum \: of \: zeros)x + (product \: of \: zeros)$

➠${x}^{2} - 6x + 4$