Q61.If p and q are non-zero real numbers and α3 + β3 = −p, αβ = q , then a quadratic equation whose roots are α2 β2 β , α is : (1) px2 −qx + p2 = 0 (2) qx2 + px + q2 = 0 (3) px2 + qx + p2 = 0 (4) qx2 −px + q2 = 0
What This Question Tests
This question tests the ability to form a new quadratic equation given its roots, requiring the use of Vieta's formulas and algebraic manipulation of sums and products of roots.
Concepts Tested
Formulas Used
x² - (sum of roots)x + (product of roots) = 0
α³+β³ = (α+β)(α²+β²-αβ)
(α+β)² = α²+β²+2αβ
📚 NCERT Sections This Tests
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
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
- Formation of quadratic equations with given roots
- Year
- 2013
- Shift
- 25 Apr Online
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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