Find the roots of the following quadratic equ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given equation: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$.To complete the square,we add and subtract the square of half the coefficient of $x$,which is $(

Vedclass · Accepted Answer

$\sqrt{3}, 1$

Vedclass · Answer

(A) Given equation: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$.To complete the square,we add and subtract the square of half the coefficient of $x$,which is $(\frac{\sqrt{3}+1}{2})^{2}$.$x^{2}-(\sqrt{3}+1) x + (\frac{\sqrt{3}+1}{2})^{2} - (\frac{\sqrt{3}+1}{2})^{2} + \sqrt{3} = 0$.$(x - \frac{\sqrt{3}+1}{2})^{2} = (\frac{\sqrt{3}+1}{2})^{2} - \sqrt{3}$.$(x - \frac{\sqrt{3}+1}{2})^{2} = \frac{3+1+2\sqrt{3}}{4} - \sqrt{3} = \frac{4+2\sqrt{3}-4\sqrt{3}}{4} = \frac{4-2\sqrt{3}}{4} = \frac{(\sqrt{3}-1)^{2}}{4}$.Taking square root on both sides: $x - \frac{\sqrt{3}+1}{2} = \pm \frac{\sqrt{3}-1}{2}$.Case $1$: $x = \frac{\sqrt{3}+1 + \sqrt{3}-1}{2} = \frac{2\sqrt{3}}{2} = \sqrt{3}$.Case $2$: $x = \frac{\sqrt{3}+1 - (\sqrt{3}-1)}{2} = \frac{\sqrt{3}+1-\sqrt{3}+1}{2} = \frac{2}{2} = 1$.Thus,the roots are $\sqrt{3}$ and $1$.

Find the roots of the following quadratic equation by the method of completing the square: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$

Similar Questions

Which of the following equations has two distinct real roots?

If one of the roots of the equation $3x^{2} + 2kx - 3 = 0$ is $-\frac{1}{2}$,then find the value of $k$.

Find the roots of the following quadratic equation by the factorisation method:
$21 x^{2}-2 x+\frac{1}{21}=0$

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $9x^{2} - 5x + 3 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module