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
RELATED QUESTIONS
Solve the following quadratic equation by factorization method: 9x2-25 = 0
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
The sum of a number and its reciprocal is 17/4. Find the number.
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
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.
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
The sum of two natural number is 28 and their product is 192. Find the numbers.
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
Solve the Following Equation : x2- x - a (a + 1) = o
A two digit number is four times the sum and 3 times the product of its digits, find the number.
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
Solve equation using factorisation method:
(2x – 3)2 = 49
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
Solve the following equation by factorisation :
2x2 + ax – a2= 0
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
