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:
(m – 3)x2 – 4x + 1 = 0
Advertisements
Solution
(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
RELATED QUESTIONS
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve the following quadratic equation by factorisation.
x2 + x – 20 = 0
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
If `sqrt (2/3)` is a solution of equation 3x2 + mx + 2 = 0, find the value of m.
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 outward journey
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
Solve the following equation by factorization
`3x - (8)/x `= 2
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.
