WBJEE · Maths · Quadratic Equation
If \(\mathrm{P}(\mathrm{x})=a \mathrm{x}^{2}+\mathrm{bx}+\mathrm{c}\) and \(\mathrm{Q}(\mathrm{x})=-\mathrm{ax}^{2}+\mathrm{dx}+\mathrm{c}\), where \(\mathrm{ac} \neq 0 \quad[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) are all real], then \(\mathrm{P}(\mathrm{x}) \cdot \mathrm{Q}(\mathrm{x})=0\) has
- A at least two real roots
- B two real roots
- C four real roots
- D no real root
Answer & Solution
Correct Answer
(A) at least two real roots
Step-by-step Solution
Detailed explanation
Hint: If \(P(x)=a x^{2}+b x+c, Q(x)=-a x^{2}+d x+c\) \(\mathrm{D}_{1}=\mathrm{b}^{2}-4 \mathrm{ac}\) \(\mathrm{D}_{2}=\mathrm{d}^{2}+4 \mathrm{ac}\) \(\Rightarrow \mathrm{D}_{1}+\mathrm{D}_{2}>0\) Atleast two real roots.
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