Question

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

Answer 1

Answer:

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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