The number of integers k for which the equation x^3-27x+k=0 has atleast two distinct integer roots is
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★ QUADRATIC RESOLUTION ★
By applying mathematical generality , we can view that , after vanishing " k " and transforming the equation to complete standard cubic equation , we can have atleast two distinct positive roots aslike -
After vanishing " k " [ k = 0 ]
x³ - 27x = 0
x [ x² - 27 ] = 0
x = 0 , x = ±3√3
Solutions obtained after implementing GENERALITY is " 3 "
HENCE , AFTER VANISHED CONSTANT , WE CAN HAVE ATLEAST TWO POSITIVE ROOTS 0 AND 3√3
THEREFORE , VALUE OF K = 0
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
By applying mathematical generality , we can view that , after vanishing " k " and transforming the equation to complete standard cubic equation , we can have atleast two distinct positive roots aslike -
After vanishing " k " [ k = 0 ]
x³ - 27x = 0
x [ x² - 27 ] = 0
x = 0 , x = ±3√3
Solutions obtained after implementing GENERALITY is " 3 "
HENCE , AFTER VANISHED CONSTANT , WE CAN HAVE ATLEAST TWO POSITIVE ROOTS 0 AND 3√3
THEREFORE , VALUE OF K = 0
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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