Solve the following quadratic equations by factorization: 3x^2-26… - Vidyadip

Question

Solve the following quadratic equations by factorization:
$3\text{x}^2-2\sqrt{6}\text{x}+2=0$

✓

Answer

We have been given
$3\text{x}^2-2\sqrt{6}\text{x}+2=0$
$3\text{x}^2-\sqrt{6}\text{x}-\sqrt{6}\text{x}+2=0$
$\sqrt{3}\text{x}\big(\sqrt{3}\text{x}-\sqrt{2}\big)-\sqrt{2}\big(\sqrt{3}\text{x}-\sqrt{2}\big)=0$
$\big(\sqrt{3}\text{x}-\sqrt{2}\big)(\sqrt{3}\text{x}-\sqrt{2})=0$
Therefore,
$\sqrt{3}\text{x}-\sqrt{2}=0$
$\sqrt{3}\text{x}=\sqrt{2}$
$\text{x}=\sqrt{\frac{2}{3}}$
Hence, $\text{x}=\sqrt{\frac{2}{3}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Which term of the $A.P. 3, 15, 27, 39, ...$ will be $120$ more than its $21^{st}$ term$?$

A kite is flying at a height of $60\ m$ above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^\circ$. Find the length of the string, assuming that there is no slack in the string.

In a $\triangle\text{ABC},$ right angled at $B, AB = 24\ cm, BC = 7\ cm.$ Determine:
$\sin \text{A}, \cos \text{A}$

The area of a triangle is $5\ sq$ units. Two of its vertices are $(2, 1)$ and $(3, -2).$ If the third vertex is $\Big(\frac{7}{2},\text{y}\Big),$ find the value of $y.$

Prove the following trigonometric identities.
If $\text{x}=\text{a}\sec\theta+\text{b}\tan\theta\text{ and y}=\text{a}\tan\theta+\text{b}\sec\theta,$ prove that $x^2-y^2=a^2-b^2$.

A girl of height $90 \ cm$ is walking away from the base of a lamp-post at a speed of $1.2 m/sec$. If the lamp is $3.6 \ m$ above the ground, find the length of her shadow after $4$ seconds.

Show that the following points are the vertices of a square:
$A(3, 2), B(0, 5), C(-3, 2)$ and $D(0, -1)$

Find the value of $k$ if points $A(k, 3), B(6, -2)$ and $C(-3, 4)$ are collinear.

If one zero of the quadratic polynomial $f(x) = 4x^2- 8kx - 9$ is negative of the other, find the value of $k.$

Find the mean of each of the following frequency distributions:

Class interval	$10-30$	$30-50$	$50-70$	$70-90$	$90-110$	$110-130$
Frequency	$5$	$8$	$12$	$20$	$3$	$2$