NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice
If p , q , r , s ∈ R, then the equation x 2 + p x + 3 q - x 2 + r x + q - x 2 + s x - 2 q = 0 has
Options
- A6 real roots
- Bat least two real roots
- C2 real and 4 imaginary roots
- D4 real and 2 imaginary roots
Correct answer
B. at least two real roots
Step-by-step solution
For real roots, p 2 - 12 q ≥ 0 ...(i) r 2 + 4 q ≥ 0 ...(ii) s 2 - 8 q ≥ 0 ...(iii) If q > 0 , then (ii) is always true. If q < 0 , then (i) and (iii) are always true. So, the equation has atleast two real roots.