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Algebra Level 4

If a a and b b are roots to the equation x 2 + x + 1 = 0 x^2+x+1=0 , then which of the following options is true?

None of these choices a = b a=b a > b a>b or b < a b<a a × b > a + b a \times b > a+b a × b > b a \times b > b a × b > a a \times b > a

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Hobart Pao
May 29, 2016

The sum of roots in quadratic equation is − b / a - b/a and product of roots in quadratic equation is c / a c/a . Obviously, − 1 < 1 -1 < 1 , so we know that a × b > a + b \boxed{a \times b > a + b }

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And why the other options are not possible?

Mateo Matijasevick - 5 years ago

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Because the relations like "greater than", "less than" are not defined in case of non-real numbers and the roots of the given equation are non-real numbers.

Sandeep Bhardwaj - 5 years ago

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Yes as complex numbers don't obey " Rule Of Tricotomy "

Aditya Narayan Sharma - 5 years ago

Thanks. My question was just to complete the answer.

Mateo Matijasevick - 5 years ago

bcoz we can not compare two complex numbers...

Deepak Sah - 4 years, 8 months ago

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