Question

if alpha and beta are zeros of the polynomial 2 X square + 5 x minus 12 then one by Alpha Plus One by beta is.....the one who answers thos will be marked as Branilest ​

Answer 1

AnsWer :

5/12.

Required Concepts :

$\tt \alpha + \beta = \frac{ - b}{a} = \frac{ \red{Coefficient \: of \: x}}{ \red{Coefficient \: of \: {x}^{2}} } .$

$\tt\alpha \beta = \frac{c}{a} = \frac{ \red{Coefficient \: of \: x}}{ \red{Constant \: term}} .$

Solution :

We have equation,

$\tt2 {x}^{2} + 5x - 12.$

Where as,

a = 2 , b= 5 and c = -12.

Sum of zeros = -b/a = -5/2.

Product of zeros = c/a = -12/2.

Now,

$\tt \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } = \frac{ \frac{ - 5}{2} }{ \frac{ - 12}{2} } .$

$= \tt - \frac{ 5}{2} \times - \frac{2}{12}$

$= \tt - \frac{ 5}{ \cancel2} \times - \frac{ \cancel2}{12}$

$= \frac{5}{12}$

Therefore, the value of 1/ alpha + 1/beta 5/12.