Question

If a and b are the roots of the polynomial x^2-x-4 then the value of 1/a+1/b-ab is
Please answer its urgent!!!

Answer 1

Question :

If a and b are the roots of the polynomial x²-x-4 then the value of 1/a +1/b -ab is.

AnsWer :

15/4

Required Concepts :

$\tt \blacksquare sum \: of \: roots \\ \tt \alpha + \beta = \frac{ - b}{a}$

$\tt \blacksquare product \: of \: roots \\ \tt \alpha \times \beta = \frac{ c}{a}$

$\blacksquare \tt \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta \\ \tt \frac{ \alpha + \beta }{ \alpha \beta } - \alpha \beta$

Solution :

We have equation,

$\tt {x}^{2} - x - 4.$

$\tt\frac{1}{a} + \frac{1}{b} - ab \\ \leadsto \tt \frac{a + b}{ab} - ab \\ \leadsto \tt \frac{1}{ - 4} + 4.$

$\leadsto \tt\frac{15}{4} .$

Therefore,the value of 1/a +1/b-ab is 15/4.