Question

Write the quadratic equation whose roots are 7 + √3 and 7 - √3 ?​

Answer 1

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Write the quadratic equation whose roots are 7 + √3 and 7 - √3 ?

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The roots are 7 + √3 , 7 − √3

Sum of the roots

=7 + √3 + 7 − √3

=14

Product of roots

=(7 + √3 )(7 − √3)

=49−3

=46

The required equation is

x²− (Sum of the roots) x + Product of roots =0

x² −14x + 46=0

Hence, the required equation is x² - 14x + 46.

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Answer 2

Answer:

The quadratic equation whose roots are 7 + √3 and 7 - √3 is

x² - 14x + 46 = 0

Step-by-step explanation:

To find,

The quadratic equation with roots  7 + √3 and 7 - √3

Recall the formula

If the roots are given, then the quadratic equation is

x² - (sum of roots)x + product of roots = 0

Solution:

Given roots are 7 + √3 and 7 - √3

Sum of roots = 7 + √3 +7 - √3 =14

Product of roots =  (7 + √3) (7 - √3) = 49 - 3 = 46

Hence the required equation is x² - (sum of roots)x + product of roots = 0

x² - 14x + 46 = 0

Hence, the quadratic equation whose roots are 7 + √3 and 7 - √3 is

x² - 14x + 46 = 0

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