If roots of equation `x^3-2c x+a b=0` are real and unequal, then prove that the roots of `x^2-2(a+b)x+a^2+b^2+2c^2=0` will be imaginary.

Explanation

Roots pf eqution `x^(2) - 2cx + ab = 0` are real and unequal
`therefore D_(1) gt 0`
`therefore 4c^(2) - 4ab gt 0`
or `c^(2) - ab gt 0` (1)
For equation `x^(2) - 2 (a + b) x + (a^(2) + b^(2) + 2c^(2))=0`
`D_(2) = 4 (a + b)^(2) - 4 (a^(2) + b^(2) + 2c^(2))`
= `- 8 ((c^(2) - ab) lt 0 (from (1))`
Therefoue , roots are imaginary.