Find the roots of the equation $x^{2} - 4 x - 9 = 0$ by the method of completing the square.

x = 4 \pm \sqrt{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 2 \pm \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 2 \pm \sqrt{6}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 2 \pm \sqrt{13}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $x = 2 \pm \sqrt{13}$
Given: $x^{2} - 4 x - 9 = 0$
This is same as:
$x^{2} - [2 \times (x) \times 2] + 2^{2} - 2^{2} - 9 = 0$
$\Rightarrow (x - 2)^{2} - 4 - 9 = 0$
$\Rightarrow (x - 2)^{2} - 13 = 0$
$\Rightarrow (x - 2)^{2} = 13$
$\Rightarrow x - 2 = \pm \sqrt{13}$
$\Rightarrow x = 2 \pm \sqrt{13}$

Suggest Corrections

Similar questions

x^{2} - 18 x + 12 = 0

5 x^{2} - 6 x - 2 = 0

Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by completion of the square method.

Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

2 x^{2} + x - 4 = 0

Join BYJU'S Learning Program