Solve the following quadratic equations by factorization: 7x+3 x … - Vidyadip

Question

Solve the following quadratic equations by factorization:
$7\text{x}+\frac{3}{\text{x}}=35\frac{3}{5}$

✓

Answer

We have been given,
$7\text{x}+\frac{3}{\text{x}}=35+\frac{3}{5}$
$7\text{x}^2+3=\Big(35+\frac{3}{5}\Big)\text{x}$
$7\text{x}^2-\Big(35+\frac{3}{5}\Big)\text{x}+3=0$
Therefore,
$7\text{x}^2-35\text{x}-\frac{3}{5}\text{x}+3=0$
$7\text{x}(\text{x}-5)-\frac{3}{5}(\text{x}-5)=0$
$\Big(7\text{x}-\frac{3}{5}\Big)(\text{x}-5)=0$
Therefore,
$7\text{x}-\frac{3}{5}=0$
$7\text{x}=\frac{3}{5}$
$\text{x}=\frac{3}{35}$
or, $\text{x}-5=0$
$\text{x}=5$
Hence, $\text{x}=\frac{3}{35}$ or $\text{x}=5$

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 "5 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Solve for x.
$\frac{\text{x}-1}{\text{x}-2}+\frac{\text{x}-3}{\text{x}-4}=3\frac{1}{3},$ $\text{x}\neq2,4$

Two cones with same base radius 8cm and height 15cm are joined together along their bases. Find the surface area of the shape formed.

The base $\text{BC}$ of an equilateral triangle $\text{ABC}$ lies on $y-$axis. The co$-$ordinates of point $C$ are $(0,3).$ The origin is the mid$-$point of the base. Find the co$-$ordinates of the point $A$ and $B.$ Also find the co$-$ordinates of another point $D$ such that $\text{BACD}$ is a rhombus.

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes to reach the destination, 1500km away in time, the pilot increased the speed by 100km/hr. Find the original speed/hour of the plane.

In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

$5x - 10y = 10$

CD and GH are respectively the bisectors of $\angle$ACB and $\angle$EGF such that D and H lie on sides AB and FE of $\triangle$ABC and $\triangle$EFG respectively. If $\triangle$ABC $\sim\triangle$FEG, show that:

$\frac{C D}{G H}=\frac{A C}{F G}$
$\triangle$DCB $\sim\triangle$HGE
$\triangle$DCA $\sim\triangle$HGF

From a point $P$ on the ground, the angle of elevation of the top of a 10 m tall building is $30^{\circ}$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point $P$. (use $\sqrt{3}=1.73$ )

Find the sum of first 100 even natural numbers which are divisible by 5.

A heap of rice in the form of a cone of diameter 9m and height 3.5m. Find the volume of rice. How much canvas cloth is required to cover the heap?

Cards bearing numbers 1, 3, 5, ..., 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing:

A prime number less than 15.
A number divisible by 3 and 5.