Question

If the root of the quadratic equation x^2 + 2px +mn= 0 are real and equal. show that the roots of the quadratic equation x^2 -2(m+n)x + (m^2 +n^2 + 2p^2 )= 0 are equal roots

Answer 1

b2 - 4ac = 0

(2p)² - 4 (mn) = 0
 4 p² = 4 mn
 
p² = mn

x² - (2m + 2n)x + (m² + n² + 2mn)

b² - 4ac = 0 => (2m + 2n)² - 4 (m² + n² + 2mn)

4m² + 8mn + 4n² - 4m² - 4n² - 8mn = 0

0 = 0 
since equation is equal to zero  roots are real and equal