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Discriminant

Find the quad...

Question

Find the quadratic equation in $x$ , whose roots are $(m + n)$ and $(m - n)$

x^{2} + 2 m x + (m^{2} + n^{2}) = 0

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x^{2} - 2 m x + (m^{2} - n^{2}) = 0

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x^{2} - m x + (m^{2} - n^{2}) = 0

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x^{2} - m n x + (m^{2} - n^{2}) = 0

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Solution

The correct option is D $x^{2} - 2 m x + (m^{2} - n^{2}) = 0$
Roots are (m+n) & (m-n)
sum of roots = m+n+m-n=2m
product of roots = (m+n)(m-n)
= $m^{2} - n^{2}$
equation
$x^{2}$ -(sum of roots)x+product of roots = 0
$x^{2} - 2 m x + m^{2} - n^{2} = 0$

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