Question

X² ‐2x+3
find alpha/beta + beta/alpha

Answer 1

QUESTION:

X² ‐2x-3 (correct question )

find alpha/beta + beta/alpha

ANSWER :

TO FIND

$\alpha \: and \: \beta$

We have to factorised the quadratic equation.

Above equation is in the form of

$a {x}^{2} + bx + c = 0$

we have to split the middle term in such a way that it's sum equal to b i.e -2 and product equal to a ×c.

${x}^{2} - 3x + x - 3$

TAKING common factor

$x(x - 3) +1(x - 3)$

$(x + 1)(x - 3) \: are \: the \: roots$

so

$x + 1 = 0 \\ x = - 1$

$\alpha = - 1$

$x - 3 = 0 \\ x= 3$

$\beta = 3$

NOW COME TO YOUR QUESTION :

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha }$

$\frac{ - 1}{3} + \frac{3}{1} \\ \frac{ - 1 + 9}{3} \\ \frac{ 8}{3}$

FINAL ANSWER

$\frac{8}{3}$

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