[JEE Advanced 1985] if p x ax 2 bx c and q x ax 2 dx c
If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$ with $ac\ne0$, then $P(x)Q(x)=0$ has at least two real roots.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Answer: True.
Discriminants sum: $(b^2-4ac)+(d^2+4ac)=b^2+d^2\ge0$, so at least one factor has real roots — hence at least two real roots overall.
JEE Advanced 1985 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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