Advertisements
Advertisements
Question
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Options
−2
2
\[- \frac{1}{2}\]
\[\frac{1}{2}\]
Advertisements
Solution
Equation is x2 − x = λ (2x − 1)
x2 – x – λ (2x – 1) = 0
x2 – (2λ + 1)x + λ = 0
Here a = 1, b = – (2λ + 1), c = λ
Sum of the roots = `– b/a`
⇒ – (– (2λ + 1)) = 0
⇒ λ = `– 1/2`
APPEARS IN
RELATED QUESTIONS
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Solve the following quadratic equations by factorization:
25x(x + 1) = -4
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
Solve the following quadratic equations by factorization:
`(3x-2)/(2x-3)=(3x-8)/(x+4)`
The sum of natural number and its positive square root is 132. Find the number.
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
x (2x + 1) = 6
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
