Question

if Alpha and Beta are the zeros of the polynomial p of x =2xsquare -5x+8 find the value of Alpha by Beta+Beta by Alpha​

Answer 1

• The quadratic equation is

$2x^{2} - 5x + 8 = 0$

Given

$given \: \alpha \: and \: \beta \: are \: the \: zeros \: of \: the \: qudratic \: eqution \: so \:$

$\alpha + \beta = \frac{ - b}{a} = \frac{5}{2}$

And

$\alpha \beta = \frac{c}{a} = \frac{8}{2} = 4$

This are the root of the quations now given that we have to find the value of

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

Which is as follows:-

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

$lcm \: is \: \alpha \beta \\ \\ = > \frac{ \alpha ^{2} + \beta ^{2} }{ \alpha \beta } \\ \\ = > \frac{ (\alpha + \beta) ^{2} - 2 \alpha \beta }{ \alpha \beta } .....(becuse \: a ^{2} + b ^{2} =( a +b) ^{2} - 2ab) \\ \\ = > \frac{ (\frac{5}{2}) ^{2} - 2 \times 4 }{4} \\ \\ = > \frac{ \frac{25}{4} - 8 }{4} \\ \\ = > \frac{ \frac{25 - 32}{4} }{4} \\ \\ = > \frac{ - 7}{16}$

The value is -7/16