Question

Find the equation whose roots are
1) 1, 2
​

Answer 1

Answer:

x^2 - 3x + 2

Step-by-step explanation:

Sum of roots = α + β = 1+2 = 3

Product of roots = αβ = 1*2 = 2

So, equation = x^2 - (α+β)x + αβ

                     = x^2 - 3x + 2

Answer 2

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$\: \blue{ \bold{ \underline{ \underline{ \: correct \: answer}}}}$

$\: \: \orange { \bold{ \underline{ \underline{step \: by \: step \: explaination : }}}}$

$\: \: \green { \bold{ \underline{ \underline{given \star}}}}$

$\: \bullet\bf{find \: the \: equation \: whose \: roots \: are}$

$\: \bf{(1) \: 1 \: and \: 2}$

$\: \red{ \bold{ \underline{ \underline{to \: find \to}}}}$

$\: \to \bf{the \: equation \: of \: \: roots \: }$

$\: \: \green { \bold{ \underline{ \underline{ \: \: solution : }}}}$

$\: \: \\ \tt : \implies the \: roots \: of \: the \: equations \: are \: 1 \: and \: 2$

$\: \: \\ \tt : \implies \: \alpha = 1 \: and \: \beta = 2.......given$

$\: \: \\ \ \tt : \implies \underline{ \: by \: formation \: of \: quadratic \: equation}$

$\: \: \\ \tt : \implies {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

$\: \: \\ \tt : \implies \underline{substitute \: the \: values \: in \: equation}$

$\: \: \\ \tt : \implies \: {x}^{2} - (1 + 2)x + 1 \times 2 = 0$

$\: \: \\ \tt : \implies \: {x}^{2} - 3x + 2 = 0$

$\: \: \\ \tt : \implies \boxed { {x}^{2} - 3x + 2 = 0 \: \: }$

______________________________________

$\: \: \: \boxed{ \bf{additional \: information}}$

$\: \bullet \bf{by \: formation \: of \: quadratic \: equation}$

$\: \ggg \bf{ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0}$

$\: : \implies \tt{sum \: of \: the \: roots \: = \frac{ - b}{a} }$

$\: \\ : \implies \tt{product \: of \: the \: roots \: = \frac{c}{a} }$