Question
Solve the following quadratic equations by factorization:
$3\sqrt{5}\text{x}^2+25\text{x}-10\sqrt{5}=0$
$3\sqrt{5}\text{x}^2+25\text{x}-10\sqrt{5}=0$
✓
Answer
$3\sqrt{5}\text{x}^2+25\text{x}-10\sqrt{5}=0$
$\sqrt{5}\bigg(3\text{x}^2+\frac{25}{\sqrt{5}}\text{x}-\frac{10\sqrt{5}}{\sqrt{5}}\bigg)=0$
$\Rightarrow\sqrt{5}\big[3\text{x}^2+5\sqrt{5}\text{x}-10\big]=0$
$\big(\text{Dividing by}\sqrt{5}\big)$
$\Rightarrow\big[3\text{x}^2-\sqrt{5}\text{x}+6\sqrt{5}\text{x}-10\big]=0$
$\Rightarrow3\text{x}^2-\sqrt{5}\text{x}+6\sqrt{5}\text{x}-10=0$
$\Rightarrow\text{x}\big(3\text{x}-\sqrt{5}\big)+2\sqrt{5}\big(3\text{x}-\sqrt{5}\big)=0$
$\Rightarrow\big(3\text{x}-\sqrt{5}\big)\big(\text{x}+2\sqrt{5}\big)=0$
Either $3\text{x}-\sqrt{5}=0,$ then $3\text{x}=\sqrt{5}$
$\Rightarrow\text{x}=\frac{\sqrt{5}}{3}$
or $\text{x}+2\sqrt{5}=0,$ then $\text{x}=-2\sqrt{5}$
$\therefore\text{x}=\frac{\sqrt{5}}{3},-2\sqrt{5}$
$\sqrt{5}\bigg(3\text{x}^2+\frac{25}{\sqrt{5}}\text{x}-\frac{10\sqrt{5}}{\sqrt{5}}\bigg)=0$
$\Rightarrow\sqrt{5}\big[3\text{x}^2+5\sqrt{5}\text{x}-10\big]=0$
$\big(\text{Dividing by}\sqrt{5}\big)$
$\Rightarrow\big[3\text{x}^2-\sqrt{5}\text{x}+6\sqrt{5}\text{x}-10\big]=0$
$\Rightarrow3\text{x}^2-\sqrt{5}\text{x}+6\sqrt{5}\text{x}-10=0$
$\Rightarrow\text{x}\big(3\text{x}-\sqrt{5}\big)+2\sqrt{5}\big(3\text{x}-\sqrt{5}\big)=0$
$\Rightarrow\big(3\text{x}-\sqrt{5}\big)\big(\text{x}+2\sqrt{5}\big)=0$
Either $3\text{x}-\sqrt{5}=0,$ then $3\text{x}=\sqrt{5}$
$\Rightarrow\text{x}=\frac{\sqrt{5}}{3}$
or $\text{x}+2\sqrt{5}=0,$ then $\text{x}=-2\sqrt{5}$
$\therefore\text{x}=\frac{\sqrt{5}}{3},-2\sqrt{5}$
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
Solve the following systems of equations:
$\text{x}+\text{y}=2\text{xy},$
$\frac{\text{x}-\text{y}}{\text{xy}}=6,\text{x}\neq0,\text{y}\neq0.$
→$\text{x}+\text{y}=2\text{xy},$
$\frac{\text{x}-\text{y}}{\text{xy}}=6,\text{x}\neq0,\text{y}\neq0.$
A T.V. manufacturer sold a T.V. to wholesaler for taxable price of ₹ 10,500. The wholeseller sold it to retailer at ₹ 12,000 taxable price and retailer sold it to customer at ₹ 14,500 taxable price. The rate of GST is 18 %, then find the CGST and SGST applicable at every transaction.
Mr. D'souza purchased 200 shares of FV Rs. 50 at a premium of Rs. 100. He received 50% dividend on the shares. After receiving the dividend he sold 100 shares at a discount of Rs. 10 and remaining shares were sold at a premium of Rs. 75. For each trade he paid the brokerage of Rs. 20. Find whether Mr. D'souza gained or incurred a loss? by how much?
Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is14 cm. Find the length of the other diagonal.
What is the probability that a leap year has 53 Sundays?
The $10^{\text {th }}$ term and the $18^{\text {th }}$ term of an A.P. are $25$ and $41$ respectively then find $38^{\text {th }}$ term of that A.P., similarly if $n^{\text {th }}$ term is $99$ . Find the value of $n$.
→Construct a $\triangle\text{ABC}$ in which AB = 5cm, $\angle\text{B} = 60^\circ,$ altitude $CD = 3cm.$ Construct a $\triangle\text{AQR}$ similar to $\triangle\text{ABC}$ such that side of $\triangle\text{AQR}$ is 1.5 times that of the corresponding sides of $\triangle\text{ABC}.$
→In the figure, O is the center of the circle. Line AQ is a tangent. If OP = 3 m(arc PM) = 120° then find the length of AP?
From a point on the roof of a house, 11 m high, it is observed that the angles of depression of the top and foot of a lamp post are 30 and 60 respectively. What is the height of the lamp post?