Download App

Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations5 Marks
Question
Solve the following quadratic equations by factorization:
$\frac{\text{x}-2}{\text{x}-3}+\frac{\text{x}-4}{\text{x}-5}=\frac{10}{3},$ $\text{x}\neq3,5$
✓

Answer

$\frac{\text{x}-2}{\text{x}-3}+\frac{\text{x}-4}{\text{x}-5}=\frac{10}{3}$
$\Rightarrow\frac{\text{x}-2}{\text{x}-3}-\frac{10}{3}=-\frac{\text{x}-4}{\text{x}-5}$
$\Rightarrow\frac{3(\text{x}-2)-10(\text{x}-3)}{3(\text{x}-3)}=-\frac{\text{x}-4}{\text{x}-5}$
$\Rightarrow\frac{3\text{x}-6-10\text{x}+30}{3\text{x}-9}=-\frac{\text{x}-4}{\text{x}-5}$
$\Rightarrow-\frac{7\text{x}-24}{3\text{x}-9}=-\frac{\text{x}-4}{\text{x}-5}$
$\Rightarrow (7x - 24)(x - 5) = (3x - 9)(x - 4)$
$\Rightarrow 7x^2 - 59x + 120 = 3x^2 - 21x + 36$
$\Rightarrow 4x^2 - 38x + 84 = 0$
$\Rightarrow 2x^2 - 19x + 42 = 0$
$\Rightarrow 2x^2 - 12x - 7x + 42 = 0$
$\Rightarrow 2x(x - 6) - 7(x - 6) = 0$
$\Rightarrow (2x - 7)(x - 6) = 0$
$\Rightarrow 2x - 7 = 0 or x - 6 = 0$
$\Rightarrow\text{x}=\frac{7}{2}$ or x = 6
Hence, the factors are 6 and $\frac{7}{2}$

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

The base QR of an equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
→
Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.
→
If the point (x, y) is equidistant from the points (a + b, b - a) and (a - b, a + b),
prove that bx = ay.
→
2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?
→
A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
→
In the following figure, ABC is a right-angled triangle,$\angle\text{B}=90^\circ,$ AB = 28cm and BC = 21cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.
→
Find the distance between the points:
$\text{P}(\text{a}\sin\alpha,\text{a}\cos\alpha)$ and $\text{Q}(\text{a}\cos\alpha, -\text{a}\sin\alpha)$
→
Find the mean, median and mode of the following data:
Classes
0-50
50-100
100-150
150-200
200-250
250-300
300-350
Frequency
2
3
5
6
5
3
1
→
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
→
The sum of two natural numbers is 28 and their product is 192. Find the numbers.
→