Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Advertisements
उत्तर
a2x2 - 3abx + 2b2 = 0
⇒ a2x2 - 2abx - abx + 2b2 = 0
⇒ ax(ax - 2b) - b(ax - 2b) = 0
⇒ (ax - b)(ax - 2b) = 0
Therefore,
ax - b = 0
ax = b
x = b/a
or,
ax - 2b = 0
ax = 2b
x = 2b/a
Hence, x = b/a or x = 2b/a
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
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 equation by factorization method : `3x^2-29x+40=0`
Find the consecutive numbers whose squares have the sum 85.
The product of two successive integral multiples of 5 is 300. Determine the multiples.
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
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 the squares of two consecutive positive integers is 365. Find the integers.
Find the two consecutive positive even integers whose product is 288.
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
If ax2 + bx + c = 0 has equal roots, then c =
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve equation using factorisation method:
(x + 3)2 – 4(x + 3) – 5 = 0
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
