Advertisements
Advertisements
Question
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also find the solution of the equation:
3x2 + 12x + (m + 7) = 0
Advertisements
Solution
3x2 + 12x + (m + 7) = 0
Here a = 3, b = 12 and c = m + 7
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` (12)2 – 4(3)(m + 7) = 0
`=>` 144 – 12m – 84 = 0
`=>` – 12m = – 60
`=>` m = 5
Put value of m in given equation
3x2 – 12x + 12 = 0
`=>` x2 + 4x + 4 = 0
`=>` (x + 2)2 = 0
`=>` x + 2 = 0
`=>` x = – 2
APPEARS IN
RELATED QUESTIONS
Solve each of the following equations by factorization:
x(x – 5) = 24
Solve the following equation : 5x2 - 11x + 2 = 0
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
(x – 3) (x + 5) = 0 gives x equal to ______.
