Question
Solve the following quadratic equation:$\text{x}^2-3\sqrt3-30=0$
✓
Answer
$\text{x}^2-3\sqrt3-30=0$$\Rightarrow\text{x}^2+5\sqrt3\text{x}-2\sqrt3\text{x}-30=0$
$\Rightarrow\text{x}\big(\text{x}+5\sqrt3\big)-2\sqrt3\big(\text{x}+5\sqrt3\big)=0$
$\Rightarrow\big(\text{x}+5\sqrt3\big)\big(\text{x}-2\sqrt3\big)=0$
$\Rightarrow\text{x}+5\sqrt3=0$ or $\text{x}-2\sqrt3=0$
$\Rightarrow\text{x}=-5\sqrt{3}$ or $\text{x}=2\sqrt3$
$\Rightarrow\text{x}\big(\text{x}+5\sqrt3\big)-2\sqrt3\big(\text{x}+5\sqrt3\big)=0$
$\Rightarrow\big(\text{x}+5\sqrt3\big)\big(\text{x}-2\sqrt3\big)=0$
$\Rightarrow\text{x}+5\sqrt3=0$ or $\text{x}-2\sqrt3=0$
$\Rightarrow\text{x}=-5\sqrt{3}$ or $\text{x}=2\sqrt3$
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 the given figure $ XY \| BC$. Find the length of $XY$.
→Solve the following quadratic equation:$3\sqrt7\text{x}^2+\text{4x}-\sqrt7=0$
→Show that the number $5 \times 11 \times 17+3 \times 11$ is a composite number.
→Four cows are tethered at four corners of a square plot of side 50m, so that they just cannot reach one another. What area will be left ungrazed?
Evaluate the following:
$\frac{\tan35^\circ}{\cot55^\circ}+\frac{\cot78^\circ}{\tan12^\circ}-1$
→$\frac{\tan35^\circ}{\cot55^\circ}+\frac{\cot78^\circ}{\tan12^\circ}-1$
On which axis do the following points lie?
Q(0, -2).
Q(0, -2).
Find the value of p for which the numbers 2p - 1, 3p + 1, 11 are in AP.
Hence, find the numbers.
Hence, find the numbers.
In the figure given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in the following:
Using prime factorization, find the $HCF$ and $LCM$ of:
$12, 15, 21$
→$12, 15, 21$
Very-short and Short-Answer Questions.
Write the value of $\big(1-\sin^2\theta\big)\sec^2\theta.$
→Write the value of $\big(1-\sin^2\theta\big)\sec^2\theta.$