Advertisements
Advertisements
Question
Which of the following is a quadratic equation?
(a) `x^3-3sqrtx+2=0` (b) `x+1/x=x^2`
(c)` x^2+1/x^2=5` (d) `2x^2-5x=(x-1)^2`
Solution
(d)`2x^2-5x=(x-1)^2`
A quadratic equation is the equation with degree 2.
∵ `2x^2-5x=(x-1)^2`
⇒ `2x^2-5x=x^2-2x+1`
⇒ `2x^2-5x-x^2+2x-1=0`
⇒` x^2-3x-1=0`, which is a quadratic equation
APPEARS IN
RELATED QUESTIONS
If the product of the roots of the equation `x^2-3x+k=10` is-2 then the value of k is
(a) -2 (b) -8 (c) 8 (d) 12
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 total cost of a certain length of a piece of cloth is Rs 200. If the piece was 5 m longer and each metre of cloth costs Rs 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre ?
Decide whether the following equation is quadratic equation or not.
y2 = 5y – 10
Decide whether the following equation is quadratic equation or not.
`"y"^2 + 1/"y" = 2`
Choose the correct answer for the following question.
Which of the following quadratic equations has roots 3,5?
Find the value of m so that the quadratic equation mx (x − 7) + 49 = 0 has two equal roots.
Which of the following is a quadratic equation ?
If 3x + 5y = 9 and 5x + 3y = 7 find the value of x + y.
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.
