Question

Find all zeroes of the polynomial x^3 - 4x^2 - 5x + 14 if two of its zeroes are (3-√2) and (3+√2)​

Answer 1

Answer :

All the zeroes are : ( 3 + √2 ), ( 3 - √2 ) and -2

Explanation :

Let one zero be α and another be β

( 3 - √2 ) = α

( 3 + √2 ) = β

Sum of zeroes = α + β

=> S = 3 + √2 + 3 - √2

=> S = 6

Product of zeroes = αβ

=> P = (3+√2)(3-√2)

=> P = 3² - 2

=> P = 9 - 2

=> P = 7

Polynomial = x² - 6x + 7

*Refer to the attachment for division*

We get, ( x + 2 ) as the factor of given polynomial,

For finding zero,

x + 2 = 0

=> x = -2

∴ All the zeroes are : ( 3 + √2 ), ( 3 - √2 ) and -2

Answer 2

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