Question

The roots of a quadratic equation are 2
& 3 respectively, find the factors &
equation. Please answer in process .

Answer 1

$\textbf{Given:}$

$\textsf{Roots are 2 and 3}$

$\textbf{To find:}$

$\textsf{Factors and equation having roots 2 and 3}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{Quadratic\;equation\;having\;roots\;\alpha\;\&\;\beta\;is}\\\\\mathsf{x^2-(\alpha+\beta)x+\alpha\beta=0}\\ \end{minipage}}$

$\mathsf{Here,\;\alpha=2\;\&\;\beta=3}$

$\textsf{The required quadratic equation is}$

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

$\mathsf{x^2-(2+3)x+(2)(3)=0}$

$\boxed{\mathsf{x^2-5x+6=0}}$

$\mathsf{x^2-5x+6}$

$\mathsf{=x^2-2x-3x+6}$

$\mathsf{=x(x-2)-3(x-2)}$

$\mathsf{=(x-2)(x-3)}$

$\therefore\textsf{The required factors are (x-2) and (x-3)}$

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