Q62.If 2 + 3i is one of the roots of the equation 2x3 −9x2 + kx −13 = 0, k ∈R, then the real root of this equation (where i2 = −1) : (1) Exists and is equal to 1 (2) Does not exist 2 (3) Exists and is equal to 1 (4) Exists and is equal to −12
What This Question Tests
This question tests the property that complex roots of a polynomial with real coefficients always occur in conjugate pairs, and the relations between roots and coefficients for a cubic equation to find the real root.
Concepts Tested
Formulas Used
If P(x) has real coefficients and (a+bi) is a root, then (a-bi) is also a root.
For ax³+bx²+cx+d=0 with roots α,β,γ: α+β+γ = -b/a, αβγ = -d/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.
5.23 — Give The Oxidation State, D Orbital Occupation And Coordination Number Of
Chemistry Class 11 · Chapter 5
5.23 Give the oxidation state, d orbital occupation and coordination number of the central metal ion in the following complexes: (i) K3[Co(C2O4)3] (iii) (NH4)2[CoF4] (ii) cis-[CrCl2(en)2]Cl (iv) [Mn(H2O)6]SO4
5.24 — Write Down The Iupac Name For Each Of The Following Complexes And Indicate
Chemistry Class 11 · Chapter 5
5.24 Write down the IUPAC name for each of the following complexes and indicate the oxidation state, electronic configuration and coordination number. Also give stereochemistry and magnetic moment of the complex: (i) K[Cr(H2O)2(C2O4)2].3H2O (iii) [CrCl3(py)3] (v) K4[Mn(CN)6] (ii) [Co(NH3)5Cl-]Cl2 (iv) Cs[FeCl4]
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Roots of polynomial equations
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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