The number of real values of ' m ' from for which the equation z 3 + ( 3 + i ) z 2 − 3 z − ( m + i ) = 0 has atleast one real root is

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z 3 + ( 3 + i ) z 2 − 3 z − ( m + i ) = 0 ​ ( z 3 + 3 z 2 − 3 z − m ) + i ( z 2 − 1 ) = 0 ​ ​ ​ ​ I f ′ 7 ′ i s a re a l roo t , t h e n z 3 + 3 z 2 − 3 z − m = 0 an d z 2 − 1 − 0 ∴ z = ± 1 z = 1 ⇒ m = 1 z = − 1 ⇒ m = 5

Mathematics - Quadratic Equation Question with Solution | TestHub

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