Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
ax2 + (4a2 − 3b)x − 12ab = 0
Advertisements
उत्तर
Given:
ax2 + (4a2 − 3b)x − 12ab = 0
ax2 + 4a2x − 3bx − 12ab = 0
ax(x + 4a) − 3b(x + 4a) = 0
(ax − 3b) (x + 4a) = 0
Therefore,
ax − 3b = 0
ax = 3b
`x=(3b)/a`
or
x + 4a = 0
x = −4a
Hence, `x=(3b)/a` or x = −4a
APPEARS IN
संबंधित प्रश्न
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
Find two numbers whose sum is 27 and product is 182.
Solve the following quadratic equations by factorization:
6x2 - x - 2 = 0
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
Two numbers differ by 3 and their product is 504. Find the number
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
Solve the following quadratic equations by factorization:
`(x + 3)^2 – 4(x + 3) – 5 = 0 `
Solve the following quadratic equations by factorization:
`(3x-2)/(2x-3)=(3x-8)/(x+4)`
`2x^2+5x-3=0`
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
Solve the following equation by factorization
3x2 – 5x – 12 = 0
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈N
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Solve the following equation by factorization
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
Find the roots of the following quadratic equation by the factorisation method:
`3sqrt(2)x^2 - 5x - sqrt(2) = 0`
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.
Using quadratic formula find the value of x.
p2x2 + (p2 – q2)x – q2 = 0
