A) 6 real roots
B) at least 2 real roots
C) 4 real toots
D) 3 real roots
Correct Answer: B
Solution :
[b] The discriminants of the given equations are \[{{D}_{1}}={{a}^{2}}+12b\], \[{{D}_{2}}={{c}^{2}}-4b\] and \[{{D}_{3}}={{d}^{2}}-8b\]. |
\[\therefore {{D}_{1}}+{{D}_{2}}+{{D}_{3}}={{a}^{2}}+{{c}^{2}}+{{d}^{2}}\ge 0\] |
Hence, at least one \[{{D}_{1}}\],\[{{D}_{2}}\],\[{{D}_{3}}\] is non-negative. Therefore, the equation has at least two real roots. |
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