Question

It the roots of the quadratic equation x²+2px+mn=o are the real and equal

Answer 1

The question is incomplete

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


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