Prove that if b^2-4c < 0, then there is no such x in R such that x^2+bx+c=0

Alexandra Richardson 2022-07-18 Answered
Prove that if b 2 4 c < 0, then there is no such x R such that x 2 + b x + c = 0
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Answers (2)

edgarovhg
Answered 2022-07-19 Author has 12 answers
Step 1
Two complex roots of a polynomial of degree 2:
a x 2 + b x + c
are given by the formula
x 1 , 2 = b ± b 2 4 a c 2 a
Step 2
and cannot be real for Δ = b 2 4 a c < 0. In you case a = 1
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przesypkai4
Answered 2022-07-20 Author has 1 answers
Step 1
Suppose there were such x. Then
0 = x 2 + b x + c = ( x b 2 ) 2 b 2 4 + c
Step 2
So ( x b 2 ) 2 = b 2 4 c = 1 4 ( b 2 4 c ) < 0
which is not possible for real numbers.
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