Question

write a quadratic equation whose roots are -3 and -2

Answer 1

(x + 3)(x + 2)

= x² + 2x + 3x + 6

= x² + 5x + 6

Answer 2

$\bold {Given:-} \begin{cases} \sf{Roots:-} \\ \sf{R_1 = - 3.} \\ \sf{R_2 = - 2.} \end{cases}$

${ \bold {\underline{Solution:-}}}$

$\underline{Let \: roots \: R_1 \: and \: R_2 \: be \: \alpha \: and \: \beta .}$

$\longrightarrow \: k{ ({x}^{2} - Sx+P)} \\ \\ \longrightarrow \: k( {x}^{2} - ( - 3 - 2)x + (- 3 \times - 2)) \\ \\ \longrightarrow \:k( {x}^{2} + 5x + 6.)$

${\large{\underline{\boxed{ k {x}^{2} + 5x + 6.}}}}$