(a - b)x² + 5(a+b) x - 2(a-b) = 0
As the roots are real and unequal ,
b² - 4ac > 0 where
a = a - b
y = 5 (a+ b)
c = -2(a - b)
So,
{5 ( a + b) }² - 4 ( a - b) ( -2 { a - b} )
25 ( a² + 2ab+ b²) + 8 ( a-b) ( a - b)
25 ( a² + 2ab + b²) + 8 ( a - b)²
25 ( a² + 2ab + b²) + 8a² - 16ab + 8b²
25a ² + 50 ab + 25b² + 8a² - 16ab+ 8b² > 0
∴ The equation has roots which are real and unequal
