Q61.Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that (1) β ∈(−1, 0) (2) |β| = 1 (3) β ∈(1, ∞) (4) β ∈(0, 1)
What This Question Tests
This question combines properties of complex numbers and quadratic equations, requiring the understanding that for real coefficients, complex roots appear in conjugate pairs, and their location on a vertical line implies specific conditions for the coefficients.
Concepts Tested
Formulas Used
Sum of roots = -b/a
Product of roots = c/a
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Roots of a quadratic equation
- Year
- 2011
- Shift
- Unknown
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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