JEE MAIN - Mathematics (2021 - 25th February Evening Shift - No. 10)
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 :
$$-$$7
7
3
$$-$$3
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
$$ \therefore $$ 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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