maths
posted by Jayden Haddy on .
prove that if m is not equal to n, the equation (m^2+n^2)x^2  2(m+n)x + 2=0 has unreal roots.

In quadratic equation:
a x ^ 2 + b x + c
expresion :
delta = b ^ 2  4 a c
is called the Discriminant
When delta > 0
There is two real root
When delta = 0
There is 2 equal real roots. ( The root is repeated. )
When delta < 0
There are two complex ( unreal ) roots.
In this case :
a = m ^ 2 + n ^ 2
b =  2 ( m + n )
c = 2
delta = b ^ 2  4 ac
delta = [  2 ( m + n ) ] ^ 2  4 * ( m ^ 2 + n ^ 2 ) * 2
delta = 4 * ( m + n ) ^ 2  8 * ( m ^ 2 + n ^ 2 )
delta = 4 * ( m ^ 2 + 2 m n + n ^ 2 )  8 m ^ 2  8 n ^ 2
delta = 4 m ^ 2 + 8 m n + 4 n ^ 2  8 m ^ 2  8 n ^ 2
delta =  4 m ^ 2 + 8 m n  4 n ^ 2
delta =  4 ( m ^ 2  2 m n + n )
delta =  4 ( m  n ) ^ 2
Becouse : ( m  n ) ^ 2 = m ^ 2  2 * m n + n ^ 2
So delta =  4 ( m  n ) ^ 2
When m > n
( m  n ) are positive
Square of positive number are positive number.
 4 * positive number are negative number
When m < n
( m  n ) are negative
Square of negative number are positive number.
 4 * positive number are negative number
This mean when m is not equal to n the Disciminant is always negative , and your equation always have two unreal roots.
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Remark :
delta is greek letter delta ( Like triangle).
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