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:
(m – 3)x2 – 4x + 1 = 0
Advertisements
उत्तर
(m – 3)x2 – 4x + 1 = 0
Here a = (m – 3), b = – 4 and c = 1
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` (– 4)2 – 4(m – 3)(1) = 0
`=>` 16 – 4m + 12 = 0
`=>` – 4m = – 28
`=>` m = 7
Put value of m in given equation
4x2 – 4x + 1 = 0
`=>` (2x – 1)2 = 0
`=>` 2x – 1 = 0
`=> x = 1/2`
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation
\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
Solve the following equation: 3x2 + 25 x + 42 = 0
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + 6x + 5 = 0; x = -1, x = -5
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
If the product of two consecutive even integers is 224, find the integers.
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
If the discriminant of the quadratic equation 3x2 - 2x + c = 0 is 16, then the value of c is ______.
