Question

can anyone please solve this Q with explanation please!! ​

Answer 1

${\huge{\boxed{\underline{\underline{\bf Given:-}}}}}$

$\sf \alpha \;\&\;\beta \; are\;zeroes\;of \;f(x)=x^2-x-4$

${\huge{\boxed{\underline{\underline{\bf To\;Find:-}}}}}$

${\boxed{\sf \dfrac{1}{\alpha}+\dfrac{1}{\beta}-\alpha\beta}}$

${\huge{\boxed{\underline{\underline{\bf Solution:-}}}}}$

$\pink\sf{We\;know\;that}$

${\boxed{\sf \alpha +\beta =\dfrac{-(b)}{a}}}$

$\sf On\;comparing\;with\;ax^2+bx+c\; we \;get$

$\sf a=1\;\&\; b=-1\;\&\;c=-4$

$\sf\implies \alpha +\beta =\dfrac{-(-1)}{1}$

$\sf\implies \alpha +\beta =\dfrac{1}{1}$

$\sf\implies \alpha +\beta =1$

${\boxed{\sf \alpha \beta =\dfrac{c}{a}}}$

$\sf\implies \alpha \beta =\dfrac{-4}{1}$

$\sf\implies \alpha \beta =-4$

$\sf Now,\;Finding$

${\boxed{\sf \dfrac{1}{\alpha}+\dfrac{1}{\beta}-\alpha\beta}}$

$\sf\dfrac{\alpha +\beta }{\alpha \beta }-\alpha \beta$

$\sf \implies\dfrac{1}{-4}-(-4)$

$\sf \implies\dfrac{-1}{4}+4$

$\sf\implies \dfrac{-1+16}{4}$

$\sf\implies\dfrac{15}4$

Answer 2

Answer:

Step-by-step explanation:

2x-1 = 1/α + 1/β - αβ. = 4.