Q81.If for some p, q, r ∈R, all have positive sign, one of the roots of the equation q2+r2 (p2 + q2)x2 −2q(p + r)x + q2 + r2 = 0 is also a root of the equation x2 + 2x −8 = 0 , then p2 is equal to-
What This Question Tests
This question tests the ability to identify common roots between two quadratic equations and use properties of roots and real coefficients to solve for an unknown parameter.
Concepts Tested
Formulas Used
If x₀ is a common root, it satisfies both equations
Discriminant D = b² - 4ac
Sum and product of 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.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
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📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of Quadratic Equations
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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