Verified answer

Answer:

i think the question is

"If the roots of the quadratic equation x²+ 2px + mn = 0 are real and equal, show that the roots of the quadratic equation

x² - 2(m+n)x + (m² + n² + 2p²)​​ = 0

are also equal."

This is the solution to the asked query :

x²+2px+mn=0

roots are real and equal

So, D=0

(2p)²-4(1)(mn)=0

4p²-4mn=0

p²-mn=0.........(1)

now

x²-2(m+n)x+(m²+n²+2p²)=0

D=(-2(m+n))²-4(1)(m²+n²+2p²)

=4(m+n)²-4(m²+n²+2p²)

=4[(m²+n²+2mn)-(m²+n²+2p²)]

=4(2mn-2p²)

=-8(0). Using (1)

=0

So x²-2(m+n)x+(m²+n²+2p²)=0

S real and equal roots

Hence proved

Step-by-step explanation: