If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i2 = $$-$$1) is a root of z2 + $$\alpha$$z + $$\beta$$ = 0, then ($$\alpha$$ $$-$$ $$\beta$$) is equal to :
JEE · Math · previous-year question
- A.$$-$$7correct
- B.7
- C.3
- D.$$-$$3
Answer
A. $$-$$7
Explanation
1 $$-$$ 2i is the root of the equation. So other root is 1 $$+$$ 2i $$ \therefore $$ Sum of roots = 1 $$-$$ 2i + 1 $$+$$ 2i = 2 = -$$\alpha $$ Product of roots = (1 $$-$$ 2i)(1 $$+$$ 2i) = 1 - 4i2 = 5 = $$\beta $$ $$ \therefore $$ $$\alpha $$ - $$\beta $$ = -2 - 5 = -7
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