Question

Find the quadratic equation whose roots are (a+b) and (a-b)

Answer 1

$Let :\alpha \:and \:beta \: are \: roots \\of \:quadratic \:equation$

$\alpha = a + b \: and \: \beta = a - b \: (given)$

$i ) Sum \:of \:the \:roots = a + b + a - b$

$\implies \alpha + \beta = 2a$

$ii ) Product \:of \:the \:roots = (a + b )( a - b)$

$\implies \alpha \beta = a^{2} - b^{2}$

$\blue { Form \: of \: a \: Quadratic \: Equation}\\\blue { whose \: roots \: \alpha \:and \:beta \: is }$

$\boxed {\pink { x^{2} - (\alpha + \beta) x + \alpha \beta = 0}}$

$\implies x^{2} - 2ax + a^{2} - b^{2} = 0$

Therefore.,

$\red { Required \: Quadratic \: Equation}\\\green { x^{2} - 2ax + a^{2} - b^{2} = 0}$

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