Question
Solve the following quadratic equation:$\text{x}^2-3\sqrt5\text{x}+10=0$
✓
Answer
$\text{x}^2-3\sqrt5\text{x}+10=0$$\Rightarrow\text{x}^2-\sqrt5\text{x}-2\sqrt{5}\text{x}+10=0$
$\Rightarrow\text{x}\big(\text{x}-\sqrt5\big)-2\sqrt5\big(\text{x}-\sqrt5\big)=0$
$\Rightarrow\big(\text{x}-\sqrt5\big)\big(\text{x}-2\sqrt5\big)=0$
$\Rightarrow\text{x}-\sqrt5=0$ or $\text{x}-2\sqrt5=0$
$\Rightarrow\text{x}=\sqrt{5}$ or $\text{x}=2\sqrt5$
$\Rightarrow\text{x}\big(\text{x}-\sqrt5\big)-2\sqrt5\big(\text{x}-\sqrt5\big)=0$
$\Rightarrow\big(\text{x}-\sqrt5\big)\big(\text{x}-2\sqrt5\big)=0$
$\Rightarrow\text{x}-\sqrt5=0$ or $\text{x}-2\sqrt5=0$
$\Rightarrow\text{x}=\sqrt{5}$ or $\text{x}=2\sqrt5$
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
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
If $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are two triangles such that $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}=\frac{3}{4},$ then write $\text{Area}(\triangle\text{ABC}):\text{Area}(\triangle\text{DEF.})$
→If $\tan\theta=\frac{20}{21},$ show that $\frac{1-\sin\theta+\cos\theta}{1+\sin\theta+\cos\theta}=\frac{3}{7}.$
→Suba Rao started work in $1995$ at an annual salary of ₹$5000$ and received a ₹$200$ raise each year. In what year did his annual salary will reach ₹$7000$?
→Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, -1 and -3 respectively.
The third term of an $A.P.$ is $7$ and the seventh term exceeds three times the third term by $2$. Find the first term, the common difference and the sum of first $20$ terms.
→The sum of two numbers is 15 . If the sum of their reciprocals is $\frac{3}{10}$, find the two numbers.
→Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height of the tower is 15m, then find the distance between the points.
In the figure, a square dart board is shown. The length of a side of the larger square is $1.5$ times the length of a side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square?
→In the given figure, $\angle$ ACB = 90° and CD $\perp$ AB. prove that $\frac { B C ^ { 2 } } { A C ^ { 2 } } = \frac { B D } { A D }$.
