Question
Solve: $4\sqrt3\text{x}^2+5\text{x}-2\sqrt3=0$
✓
Answer
$4\sqrt3\text{x}^2+5\text{x}-2\sqrt3=0$$\Rightarrow4\sqrt3\text{x}^2+\text{8x}-\text{3x}-2\sqrt3=0$
$\Rightarrow\text{4x}\big(\sqrt3\text{x}+2\big)-\sqrt3\big(\sqrt3\text{x}+2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}+2\big)\big(4\text{x}-\sqrt3\big)=0$
$\Rightarrow\sqrt3\text{x}+2=0$ or $4\text{x}-\sqrt3=0$
$\Rightarrow\text{x}=-\frac{2}{\sqrt3}=-\frac{2\sqrt3}{3}$ or $\text{x}=\frac{\sqrt3}{4}$
$\Rightarrow\text{4x}\big(\sqrt3\text{x}+2\big)-\sqrt3\big(\sqrt3\text{x}+2\big)=0$
$\Rightarrow\big(\sqrt3\text{x}+2\big)\big(4\text{x}-\sqrt3\big)=0$
$\Rightarrow\sqrt3\text{x}+2=0$ or $4\text{x}-\sqrt3=0$
$\Rightarrow\text{x}=-\frac{2}{\sqrt3}=-\frac{2\sqrt3}{3}$ or $\text{x}=\frac{\sqrt3}{4}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In $\Delta$DEF, line PQ || side EF. DQ = 1.8, QF = 5.4, PE = 7.2. Find DE.
→Write the area of the sector of a circle whose radius is r and length of the arc is l.
Prove that angles inscribed in the same arc are congruent.
Given: In a circle with center $C, \angle P Q R$ and $\angle P S R$ are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: $\angle P Q R \cong \angle P S R$.
Proof:
$ m \angle PQR =\frac{1}{2} \times[ m (\operatorname{arc} PTR )]$
$m \angle \square=\frac{1}{2} \times[ m (\operatorname{arc} PTR )] \ldots . . . \text { (ii) } \square$
$m \angle \square= m \angle PSR \quad \ldots . . .[ By \text { (i) and (ii) }]$
$\therefore \angle PQR \cong \angle PSR $
→Given: In a circle with center $C, \angle P Q R$ and $\angle P S R$ are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: $\angle P Q R \cong \angle P S R$.
Proof:
$ m \angle PQR =\frac{1}{2} \times[ m (\operatorname{arc} PTR )]$
$m \angle \square=\frac{1}{2} \times[ m (\operatorname{arc} PTR )] \ldots . . . \text { (ii) } \square$
$m \angle \square= m \angle PSR \quad \ldots . . .[ By \text { (i) and (ii) }]$
$\therefore \angle PQR \cong \angle PSR $
In the given figure, PA and PB are the tangents to a circle with centre O. Show that the points A, O, B, P are concyclic.
Evaluate the following:
$\text{cosec 31}^\circ-\sec59^\circ$
→$\text{cosec 31}^\circ-\sec59^\circ$
In the following figure, ABCD is a rectangle, having $AB = 20\ cm$ and $BC = 14\ cm$. Two sectors of $180^\circ $ have been cut off. Calculate: The area of the shaded region.
→Find the indicated terms in the following sequences whose $n^{th}$ terms are:
$a_n = 5n - 4; a_{12}$ and $a_{15}.$
→$a_n = 5n - 4; a_{12}$ and $a_{15}.$
In figure 3.76, seg PQ is a diameter of a circle with centre O. R is any point on the circle. seg RS⊥seg PQ.
Prove that, SR is the geometric mean of PS and SQ. [That is, SR² = PS ×SQ]
Prove that, SR is the geometric mean of PS and SQ. [That is, SR² = PS ×SQ]
The given sequence is AP or not ? If they are A.P. find the common difference.
$0, – 4, – 8, – 12, . . .$
→$0, – 4, – 8, – 12, . . .$
‘M/s. Real Paint’ sold 2 tins of lustre paint and taxable value of each tin is Rs. 2800. If the rate of GST is 28%, then find the amount of CGST and SGST charged in the tax invoice.