Multiple choice

If $a,b,c,r \in R$, then the equation $(x^2+ax-3b)(x^2-cx+b)(x^2-dx+2b)=0$ has

  1. $6$ real roots
  2. at least $2$ real roots
  3. $4$ real roots
  4. $3$ real roots
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If b < 0, the second quadratic has discriminant c^2 - 4b > 0, so it has two real roots. If b >= 0, the first quadratic has discriminant a^2 + 12b >= 0, giving real roots under the usual multiplicity convention. Thus, at least two real roots are guaranteed.

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