Q62.If the two roots of the equation, (a −1) (x4 + x2 + 1) + (a + 1)(x2 + x + 1) 2 = 0 are real and distinct, then the set of all values of a is equal to (1) (0, 12 ) (2) (−12 , 0) ∪(0, 12 ) (3) (−∞, −2) ∪(2, ∞) (4) (−12 , 0)
What This Question Tests
This question tests the ability to factor complex algebraic expressions and then apply the discriminant condition for real and distinct roots of a quadratic equation. It also requires careful consideration of the coefficient of the quadratic term.
Concepts Tested
Formulas Used
x^4 + x^2 + 1 = (x^2+x+1)(x^2-x+1)
D = b^2 - 4ac > 0 for real and distinct roots
📚 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.
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.
5.16 — Draw Figure To Show The Splitting Of D Orbitals In An Octahedral Crystal Field.
Chemistry Class 11 · Chapter 5
5.16 Draw figure to show the splitting of d orbitals in an octahedral crystal field.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Nature of Roots
- Year
- 2015
- Shift
- 11 Apr Online
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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