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 the following quadratic equations
(i) 7x2 = 8 – 10x
(ii) 3(x2 – 4) = 5x
(iii) x(x + 1) + (x + 2) (x + 3) = 42
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
Find the two consecutive positive even integers whose product is 288.
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
Find two consecutive integers such that the sum of their squares is 61
Find three consecutive odd integers, the sum of whose squares is 83.
