Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
ax2 + (4a2 − 3b)x − 12ab = 0
Advertisements
Solution
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
RELATED QUESTIONS
Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
Find the consecutive numbers whose squares have the sum 85.
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Solve the following quadratic equations by factorization:
`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Find two consecutive multiples of 3 whose product is 648.
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
Solve the following equation:
(2x+3) (3x-7) = 0
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
In each of the following determine whether the given values are solutions of the equation or not.
x2 + 6x + 5 = 0; x = -1, x = -5
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
Two pipes running together can fill a tank in `11(1)/(9)` minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would/fill the tank.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
