Q52.Let α and β be the roots of x2 −3x + p = 0 and γ and δ be the roots of x2 −6x + q = 0. If α, β, γ, δ from a geometric progression. Then ratio (2 q + p) : (2 q −p) is (1) 3 : 1 (2) 9 : 7 (3) 5 : 3 (4) 33 : 31
What This Question Tests
This question requires combining the properties of roots of quadratic equations with the relationships between terms in a geometric progression to find a desired ratio.
Concepts Tested
Formulas Used
For ax²+bx+c=0, roots α,β: α+β = -b/a, αβ = c/a
Terms of a G.P.: a, ar, ar², ar³
📚 NCERT Sections This Tests
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
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.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of quadratic equation and geometric progression
- Year
- 2020
- Shift
- 04 Sep Shift 1
- Q Number
- Q52
- Type
- MCQ
- NCERT Ref
- Class 10 Mathematics Ch 4: Quadratic Equations; Class 11 Mathematics Ch 9: Sequences & Series
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