Advertisements
Advertisements
प्रश्न
Find the roots of the following quadratic equation by the factorisation method:
`2/5x^2 - x - 3/5 = 0`
Advertisements
उत्तर
Given equation is `2/5x^2 - x - 3/5` = 0
On multiplying by 5 on both sides, we get
2x2 – 5x – 3 = 0
⇒ 2x2 – (6x – x) – 3 = 0 ....[By splitting middle term]
⇒ 2x2 – 6x + x – 3 = 0
⇒ 2x(x – 3) + 1(x – 3) = 0
⇒ (x – 3)(2x + 1) = 0
Now, x – 3 = 0
⇒ x = 3
And 2x + 1 = 0
⇒ x = `-1/2`
Hence, the roots of the equation 2x2 – 5x – 3 = 0 are `- 1/2` and 3.
APPEARS IN
संबंधित प्रश्न
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.
`x^2-6x+3=0`
`x^2+8x-2=0`
`2x^2+5x-3=0`
Determine whether the values given against the quadratic equation are the roots of the equation.
2m2 – 5m = 0, m = 2, `5/2`
Solve the following quadratic equation by factorisation.
25m2 = 9
Find the values of p for which the quadratic equation
If the equation ax2 + 2x + a = 0 has two distinct roots, if
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve the following equation by factorization
4x2 = 3x
Find three successive even natural numbers, the sum of whose squares is 308.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
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.
