Question

$\alpha and\beta \text{are the zeroes of the quadratic}\text{polynomial},f\left(x\right)=x^2-5x+4.\text{Find out the value of}\frac{1}{\alpha }+\frac{1}{\beta }-2\alpha \beta ?$

• A.
  $-27/4$
• B.
  $27/4$
  
• C.
  $25/2$
• D.
  $-25/2$

Answer 1

The correct option is A

$-27/4$
$f\left(x\right)=x^2-5x+4\alpha +\beta =\frac{-b}{a}=-\frac{(-5)}{1}=5\alpha \beta =\frac{c}{a}=\frac{4}{1}=4\frac{1}{\alpha }+\frac{1}{\beta }-2\alpha \beta =\frac{\beta +\alpha -2(\alpha \beta {)}^2}{\alpha \beta }=\frac{5-2(4{)}^2}{4}=\frac{5-32}{4}=\frac{-27}{4}\therefore \frac{1}{\alpha }+\frac{1}{\beta }-2\alpha \beta =-\frac{27}{4}$