Question

If $\alpha ,\beta$ are zeroes of $x^2-4x+1,$ then $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta$ is :

• A. $3$
• B. $5$
• C. $-5$
• D. $-3$

Answer 1

Answer: (A)

$3$

Given: $\alpha ,\beta$ are zeroes of $x^2-4x+1$

To find value of $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta$

We know, $\alpha +\beta =4$ ........ $\left(i\right)$

$\alpha \beta =1$ .......... $\left(ii\right)$

$\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta =\frac{\alpha +\beta }{\alpha \beta }-\alpha \beta$

$=\frac{4}{1}-1=3$ ...... [From equation $\left(i\right)$ and $\left(ii\right)$]

Hence, $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta =3$