Question

Question 1 (vii)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

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

Answer 1

Given equation is $\frac{1}{2}{x}^2-\sqrt{11}x+1=0$
On comparing with ax2 + bx + c = 0, we get
$a=\frac{1}{2}b=-\sqrt{11}andc=1$
$\therefore$ by quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$=\frac{-(-1\sqrt{11})\pm \sqrt{(-\sqrt{11}{)}^2}-4\times \frac{1}{2}\times 1}{2\left(\frac{1}{2}\right)}$
$=\frac{\sqrt{11}\pm \sqrt{11-2}}{1}=\sqrt{11}\pm \sqrt{9}$
$=\sqrt{11}\pm 3=3+\sqrt{11},\sqrt{11}-3$
So, 3 + $\sqrt{11}$ and $\sqrt{11}$ - 3 are the roots of the given equation