Can someone solve this problem?

Question

If the Quadratic equation αx2 + βx + a2 + b2 + c2 – ab – bc – ca = 0 has imaginary roots, then

1. 2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 > 0
2. 2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0
3. 2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 = 0
4. none of these

Answer 1

for a quadratic equation to have imaginary roots, the following equation must be satifised ie

b^2 -4ac<0

from the above, simply sub in the coefficients to test whether the equation is satifised.

β^2- 4α(a2+b2+c2-ab-bc-ca) < 0

Thus you can see, the quadratic equation has imaginary roots. however, the correct answer is not in one of the options.

as such, the answer is option 4.

Answer 2

β^2- 4α(a2+b2+c2-ab-bc-ca) < 0
None of the above

Answer 3

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