Advertisements
Advertisements
प्रश्न
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
Advertisements
उत्तर
x2 – (m + 2)x + (m + 5) = 0
Here a = 1, b = – 4(m + 2) and c = m + 5
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` [–(m + 2)]2 – 4(1)(m + 5) = 0
`=>` m2 + 4m + 4 – 4m – 20 = 0
`=>` m2 – 16 = 0
`=>` m2 = 16
`=>` m = ±4
Put value of m in given equation
x2 – 6x + 9 = 0 or x2 + 2x + 1 = 0
`=>` (x – 3)2 = 0 or (x + 1)2 = 0
`=>` x – 3 = 0 or x + 1 = 0
`=>` x = 3 or x = –1
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`4sqrt3x^2+5x-2sqrt3=0`
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Solve the following quadratic equations by factorization:
`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
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.
Solve the following equation by factorisation :
2x2 + ax – a2= 0
A dealer sells a toy for ₹ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.
