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Algebra Level 4

$(x^2+ax-3b)(x^2-cx+b)(x^2-dx+2b) = 0$

For real numbers $a,b,c$ and $d$ , the equation above has:

At most 2 real roots At least 2 real roots At most 4 real roots 4 real roots At least 4 real roots 3 real roots 6 real roots

1 solution

Venkata Karthik Bandaru
Jan 11, 2016

Hint : Observe that there are $3$ groupings of quadratic expressions. Compute their discriminants, add them, observe that the sum is positive.Hence, atleast one of the discriminants must be positive, i.e. atleast one of the groupings can be factored into $2$ linear expressions in $\mathbb{R}$ , hence there are atleast 2 real roots for the given equation.

correct!!!

Atul Shivam - 5 years, 5 months ago

Did the same way.

Aditya Sky - 5 years, 4 months ago

Don't report this problem if you are getting this wrong

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