WBJEE · Maths · Quadratic Equation
If \(P(x)=a x^2+b x+c\) and \(Q(x)=-a x^2+d x+c\) where \(a c \neq 0\), then \(P(x) \cdot Q(x)=0\) has \((a, b, c, d\) are real)
- A 2 real roots
- B at least two real roots
- C 4 real roots
- D no real root
Answer & Solution
Correct Answer
(B) at least two real roots
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint: } D_1=b^2-4 a c \\ & D_2=d^2+4 a c \\ & D_1+D_2=b^2+d^2\gt0 \\ & D_1+D_2\gt0 \end{aligned}\) At least one of \(D_1\) or \(D_2\) is +ve so at least two real roots
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