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प्रश्न
Find the roots of the quadratic equation `2x^2-x-6=0`
The roots of the quadratic equation 2x2 − x − 6 = 0 are
पर्याय
A.`-2,3/2`
B.`2,-3/2`
C.`-2,-3/2`
D.`2,3/2`
उत्तर
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`
संबंधित प्रश्न
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 roots of the equation` ax^2+bx+c=0` are equal then c=?
(a)`b/(2a)` (b) `b/(2a)` (c) `-b^2/(4a)` (d) `B^2/(4a)`
If the equation `9x^26kx+4=0` has equal roots then k =?
(a)1 or (b)-1 or 4 (c)1 or -4 (d)-1 or -4
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`
Show the x= -3 is a solution of `x^2+6x+9=0`
Solve` 2x^2+ax-a^2=0`
Choose the correct answer for the following question.
\[\sqrt{5} m^2 - \sqrt{5}m + \sqrt{5} = 0\] which of the following statement is true for this given equation?
Alka spends 90 % of the amount sent to her and saves Rs. 120 per month. Find the amount sent to her per month.
Find c if the system of equations cx+3y+(3 - c ) = 0, 12x + cy - c = 0 has infinitely many solutions?
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.
