Advertisements
Advertisements
Questions
Find the roots of the quadratic equation `2x^2-x-6=0`
The roots of the quadratic equation 2x2 − x − 6 = 0 are
Options
A.`-2,3/2`
B.`2,-3/2`
C.`-2,-3/2`
D.`2,3/2`
Solution
The given quadratic equation is `2x^2-x-6=0`
`2x^2-x-6=0`
⇒`2x^2-4x+3x-6=0`
⇒` 2x(x-2)+3(x-2)=0`
⇒`(x-2)(2x+3)=0`
⇒`x-2=0 or 2x+3=0`
⇒ `x=2 or x=-3/2`
Hence, the roots of the given equation are` 2 and -3/2`
RELATED QUESTIONS
The sum of the roots of the equation` x^2-6x+2=0`
(a) 2 (b)-2 (c)6 (d)-6
If the sum of the roots of the equation `kx^2+2x+3k=0` is equal to their product then the value of k
`(a) 1/3 (b)-1/3 (c)2/3 (d)-2/3`
If `x=-1/2` is a solution of the quadratic equation `3x^2+2kx-3=0`
Find the value of k.
Find the solution of the quadratic equation `3sqrt3x^2+10x+sqrt3=0`
Solve `x^2+6x-(a^2+2a-8)=0`
Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is `1/3` of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.
If 3x + 5y = 9 and 5x + 3y = 7 find the value of x + y.
Solve the following quadratic equation :
x2 +8x + 15 = 0
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.
