Find the roots of the quadratic equations by using the quadratic formula in each of the following:
$ \frac{1}{2} x^{2}-\sqrt{11} x+1=0 $

AcademicMathematicsNCERTClass 10


Given quadratic equation is \( \frac{1}{2} x^{2}-\sqrt{11} x+1=0 \).

To do:

We have to find the roots of the given quadratic equation.


\( \frac{1}{2} x^{2}-\sqrt{11} x+1=0 \)

The above equation is of the form $ax^2 + bx + c = 0$, where $a = \frac{1}{2}, b = -\sqrt{11}$ and $c =1$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(-\sqrt{11})^{2}-4 \times \frac{1}{2} \times 1$




Let the roots of the equation are $\alpha$ and $\beta$

$\alpha =\frac{-b+\sqrt{\mathrm{D}}}{2 a}$




$\beta =\frac{-b-\sqrt{\mathrm{D}}}{2 a}$




Hence, the roots of the given quadratic equation are $3+\sqrt{11}, -3+\sqrt{11}$. 

Updated on 10-Oct-2022 13:27:26