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Question

If a,b,c,dR, then the equation (x2+ax3b)(x2cx+b)(x2dx+2b)=0 has

A
no real roots
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B
at least two real roots
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C
at least four real roots
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D
exactly six real roots
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Solution

The correct option is B at least two real roots
The discriminants of the given quadratic factors are
D1=a2+12b,D2=c24b and D3=d28b
D1+D2+D3=a2+c2+d20
Hence, at least one of D1,D2,D3 is non-negative.
Therefore, the equation has at least two real roots.

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