Question

1/2 , -1/2 Form the quadratic equation from the given roots

Answer 1

Here's the answer............

$the \: quadratic \: equation \:in \: x \: is \: given \: by \: \\ (x - \alpha )(x - \beta ) \: where \: \alpha \: and \: \beta are \: the \: roots\\ \: \: \: \: \: \: (x - ( \frac{1}{2} ))(x - ( \frac{ - 1}{2} )) \\ = (x - \frac{1}{2} )(x + \frac{1}{2} ) \\ = {x}^{2} - \frac{1}{4} \\ = \frac{1}{4} ( 4{x}^{2} - 1)$

Answer 2

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Quadratic equation whose roots

are m , n is

x² - ( m+n)x + mn

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Here ,

m = 1/2 , n = -1/2 ,

i ) sum of the roots = m+n

= 1/2 - 1/2 = 0

ii ) product of the roots

= ( 1/2 )( -1/2 )

= -1/4

Therefore ,

Required Quadratic equation,

x² - 0×x + ( -1/4 ) = 0

=> x² - 1/4 = 0

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