Advertisements
Advertisements
Question
If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor.
Solution
Suppose divisor = x
∴ Quotient= 9x + 2
Dividend = 460 and remainder = 5
Dividend = Divisor × Quotient + Remainder
∴ 460 = x × (9x + 2) + 5
∴ 460 = 9x2 + 2x + 5
∴ 9x2 + 2x + 5 – 460 = 0
∴ 9x2 + 2x – 455 = 0
∴ 9x2 – 63x + 65x – 455 = 0
∴ 9x(x – 7) + 65(x – 7) = 0
∴ (9x + 65)(x – 7) = 0
∴ 9x + 65 = 0 or x – 7 = 0
∴ x = `(-65)/9` or x = 7
However, 460 is divided by a natural number, which cannot be negative.
∴ x = 7
∴Divisor = 7
∴ Quotient = 9 × 7 + 2 = 63 + 2 = 65
∴ Quotient is 65 and divisor is 7.
APPEARS IN
RELATED QUESTIONS
The sum of the roots of the equation` x^2-6x+2=0`
(a) 2 (b)-2 (c)6 (d)-6
If one root of the equation` 3x^2-10x+3=0 is 1/3` then the other root is
(a) `-1/3` (b) `1/3` (c)`-3` (d)`3`
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`
In the equation `ax^2+bx+c=0` it is given that `D=(b^2-4ac)>0`
equation are
(a) real and equal (b) real and unequal (c) imaginary (d) none of these
The length of a rectangular field exceeds its breadth by 8 m and the area of the field is `240 m^2` . The breadth of the field is
(a) 20 m (b) 30 m (c) 12 m (d) 16 m
The roots of the quadratic equation `2x^2-x-6=0`
(a)`-2, 3/2` (b) `2, -3/2`
(c)` -2, 3/2` (d) `2, 3/2`
Find the value of k for which the quadratic equation `9x^2-3kx+k=0` has equal roots.
Solve` 2x^2+ax-a^2=0`
Solve `sqrt3x^2+10x-8sqrt3=0`
Decide whether the following equation is quadratic equation or not.
(m + 2) (m – 5) = 0
In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart.
Choose the correct answer for the following question.
The roots of x2 + kx + k = 0 are real and equal, find k.
Choose the correct answer for the following question.
Which of the following quadratic equations has roots 3,5?
Solve the following quadratic equation.
`1/(x + 5) = 1/x^2`
Solve the following quadratic equation.
\[x^2 - \frac{3x}{10} - \frac{1}{10} = 0\]
Solve the following quadratic equation.
5m2 + 2m + 1 = 0
Solve any two of the following.
Solve : `3x+y=14 ; x-y=2`
For the quadratic equation 3x2 + 2x - 1 = 0 , find the value of the discriminant.
The ratio of fruit trees and vegetable trees in an orchard is 3:4. If 6 more trees of each type are planted, the ratio of trees would be 6:7. Find the number of fruit trees and vegetable trees in the orchard.
The ratio of fruit trees and vegetable trees = 3:4
So, let the number of fruit trees= 3x and the number of vegetable trees = `square`
From the given condition,
`(3x + square)/(square + square) = square/square`
`square (3x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
`square = square`
x = `square`
∴ Number of fruit trees in the orchard = 3x = 3 × `square` = `square` and number of vegetable trees in the orchard = 4x = 4 × `square` = `square`
Hence, the number of fruit trees and vegetable trees in the orchard are `square` and `square` respectively.
If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval is ______.
