Advertisements
Advertisements
Question
In an orchard there are total 200 trees. If the number of trees in each column is more by 10 than the number of trees in each row, then find the number of trees in each row
Solution
Let the number of trees in each row be x.
The number of trees in each column is more by 10 than the number of trees in each row.
∴ The number of trees in each column will be x + 10.
According to the given condition,
There is a total of 200 trees.
∴ x(x + 10) = 200
∴ x2 + 10x – 200 = 0
∴ x2 + 20x – 10x – 200 = 0
| -200 |
| 20 -10 |
| 20 × (-10) = -200 |
| 20 - 10 = 10 |
∴ x(x + 20) – 10(x + 20) = 0
∴ (x + 20)(x – 10) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
x + 20 = 0 or x – 10 = 0
∴ x = – 20 or x = 10
But, the number of trees cannot be negative.
∴ x = 10
∴ The number of trees in each row is 10.
APPEARS IN
RELATED QUESTIONS
If one of the roots of the quadratic equation x2 - 11x + k = 0 is 9, then find the value of k
If one root of `5x^2+13x+k=0` be the reciprocal of the other root then the value of k is
`(a)0 (b)1 (c)2 (d)5`
If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a)`x^2-6x+6=0` (b)` x^2+6x+6=0` (c)`x^2-6x-6=0` (d)`x^2+6x+6=0`
If the equation `4x^2-3kx+1=0` has equal roots then value of k=?
(a)`+-2/3` (b)`+-1/3`
(c)` +-3/4` (d) `+-4/3`
The roots of the equation 2x^2-6x+7=0 are
(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary
The sum of a number and its reciprocal is `2 1/20` The number is
(a) `5/4 or 4/5` (b)`4/3 or 3/4`
(c) `5/6 or 6/5` (d) `1/6 or 6`
If `x=-1/2` is a solution of the quadratic equation `3x^2+2kx-3=0`
Find the value of k.
If the roots of the quadratic equation `2x^2+8x+k=0` are equal then find the value of k.
Solve `sqrt3x^2-2sqrt2x-2sqrt3=0`
Solve` 4sqrt3x^2+5x-2sqrt3=0`
Solve `x^2+5x-(a^2+a-6)=0`
If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals: ?
Decide whether the following equation is quadratic equation or not.
`"y"^2 + 1/"y" = 2`
Write the following equation in the form ax2 + bx + c = 0, then write the values of a, b, c for the equation.
(x – 1)2 = 2x + 3
Write the following equations in the form ax2 + bx + c= 0, then write the values of a, b, c for each equation.
p(3+6p) = –5
Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
Solve the following quadratic equation.
5m2 + 2m + 1 = 0
Find c if the system of equations cx+3y+(3 - c ) = 0, 12x + cy - c = 0 has infinitely many solutions?
For the quadratic equation 3x2 + 2x - 1 = 0 , find the value of the discriminant.
Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.
