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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
विकल्प
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 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`
The roots of the equation `ax^2+bx+c=0` will be reciprocal each other if
(a)a=b (b)b=c (c)=a (d)= none of these
If the roots of` 5x^2-k+1=0` are real and distinct then
(a)`-2sqrt5<k2<sqrt5` (b)` k>2sqrt5 ` only
(c)` k<-2sqrt5` (d) either `k>2sqrt5 or k<-2sqrt5`
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`
If one root of the quadratic equation `3x^2-10x+k=0` is reciprocal of the other , find the value of k.
Solve for x: `3x^2-2sqrt6x+2=0`
Solve the following quadratic equation :
x2 +8x + 15 = 0
Find c if the system of equations cx+3y+(3 - c ) = 0, 12x + cy - c = 0 has infinitely many solutions?
Present age of mother of Manish is 1 year more than 5 times the present age of Manish. Four years before, if the product of their ages was 22, then find the present age of Manish and his mother
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.
