Q60 / 90 · JEE Main 2021 (25 Feb Shift 2) · Mathematics

If $α, β \in R$ are such that $1 - 2 i$ (here $i^{2} = - 1$ ) is a root of $z^{2} + α z + β = 0$ , then $(α - β)$ is equal to:

Correct answer
A
$- 7$
B
$7$
C
$- 3$
D
$3$

Solution

$∵ α, β \in R \Rightarrow$ other root is $1 + 2 i$

$α = -$ ( sum of roots ) $= - (1 - 2 i + 1 + 2 i) = - 2$

$β =$ product of roots $= (1 - 2 i) (1 + 2 i) = 5$

$∴ α - β = - 7$

option $(1)$

Hence, the correct answer is option: 'A'.

Relevant Questions

Let one root of the quadratic equation in : be twice the other. Then the length of the latus rectum of the parabola is equal to:06 Apr, 2026 (M)Relation between Roots and Coefficients
Consider the quadratic equation , . Let be the minimum value of the product of its roots and be the maximum value of the sum of its roots. T06 Apr, 2026 (E)Relation between Roots and Coefficients
Let . Let be the roots of the equation . If and , then is equal to:05 Apr, 2026 (M)Relation between Roots and Coefficients
Let , where , be the roots of the quadratic equation . Then is equal to:05 Apr, 2026 (M)Relation between Roots and Coefficients
Let be the roots of the equation and be the roots the equation ; . If are in G.P., then equals :05 Apr, 2026 (E)Relation between Roots and Coefficients
If and , where are two roots of the equation , , then is equal to:04 Apr, 2026 (E)Relation between Roots and Coefficients