Question:medium
If \(P(x) = ax^2 + bx + c\) and \(Q(x) = -ax^2 + dx + c\) where \(ac \neq 0\), then \(P(x) \cdot Q(x) = 0\) has:
If \(P(x) = ax^2 + bx + c\) and \(Q(x) = -ax^2 + dx + c\) where \(ac \neq 0\), then \(P(x) \cdot Q(x) = 0\) has:
Show Hint
When subtracting quadratic equations, always simplify and factor the terms to identify the real roots. In this case, factoring helped us identify the roots clearly.
Updated On: Nov 28, 2025
- 2 real roots
- at least two real roots
- 4 real roots
- no real roots
Top Questions on Quadratic Equation
- If the quadratic equation \( ax^2 + bx + c = 0 \) (\( a > 0 \)) has two roots \( \alpha \) and \( \beta \) such that \( \alpha < -2 \) and \( \beta > 2 \), then:
- WBJEE - 2024
- Mathematics
- Quadratic Equation
- If \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]- WBJEE - 2024
- Mathematics
- Quadratic Equation
- The equation \(2x^5 + 5x = 3x^3 + 4x^4\) has:
- WBJEE - 2024
- Mathematics
- Quadratic Equation
- If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:
- WBJEE - 2024
- Mathematics
- Quadratic Equation
- Want to practice more? Try solving extra ecology questions todayView All Questions