Question

Solve it as fast as u can plz urgent

Answer 1

Heya !!!


F( X ) = X⁴ - 6X³ - 26X² + 138X - 35


Let ,


Alpha = ( 2 + ✓3 ) and Beta = ( 2 - ✓3 )


Then,


Alpha + Beta = ( 2 + ✓3 ) + ( 2 - ✓3 ) = (4)


And,


Alpha × Beta = ( 2 + ✓3 ) ( 2 - ✓3 ) = (2)² - (✓3)² = 4-3 = 1

So, the quadratic polynomial whose zeroes are alpha and beta is Given by


X² - ( Sum of zeroes)X + Product of zeroes


=> X² - 4X + 1


Therefore,


( X² - 4X + 1 ) is a factor of P(X).


On dividing P(X ) by X²-4X + 1 , we get



Quotient = X²-2X - 35




==> X² - 2X -35



=> X² - 7X + 5X - 35



=> X ( X - 7 ) + 5 ( X - 7 )



=> ( X- 7 ) ( X + 5 ) = 0



=> X = 7 OR X = -5



Hence,

7 and -5 , ( 2 + ✓3 ) and ( 2 - ✓3 ) are four zeroes of the given polynomial.


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