Q61.Let p, q ∈ Q . If 2 −√3 is a root of the quadratic equation x2 + px + q = 0, then (1) p2–4q + 12 = 0 (2) q2 + 4p + 14 = 0 (3) p2–4q–12 = 0 (4) q2–4p–16 = 0
What This Question Tests
This question tests the understanding that irrational roots of a quadratic equation with rational coefficients appear in conjugate pairs. Using this property, both roots can be identified, and subsequently, the coefficients p and q can be found using Vieta's formulas to determine the correct option.
Concepts Tested
Formulas Used
If p,q are rational, and a+√b is a root of Ax²+Bx+C=0, then a-√b is also a root.
Sum of roots = -p/1
Product of roots = q/1
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of quadratic equation
- Year
- 2019
- Shift
- 09 Apr Shift 1
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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