Question

If the sum of the roots of the equation x²– x = λ (2x – 1) is zero, then λ =
A. – 2
B. 2
C. -1/2
D.1/2

Answer 1

If the sum of the roots of the equation x²– x = λ (2x – 1) is zero, then λ is equal to - 1 / 2. Hence, option (C) is correct.

• The given quadratic equation is x² - x = λ (2x – 1)

=> x² - x - λ (2x – 1) = 0

=> x² - x - 2λx + λ = 0

=> x² - x (1 + 2λ) + λ = 0

=> x² - (1 + 2λ) x + λ = 0

• The sum of the roots of a quadratic equation is given as (- b / a), where b is the coefficient of x and a is the coefficientof x².

 ∴ a =1,  b = - (1 + (1 + 2λ))

 

• According to the question,

- b / a = 0

=> - { - (1 + 2λ) } / 1 = 0

=> 1 + 2λ = 0

=> 2λ = - 1

=> λ = - 1 / 2

 ∴ The value of λ in the given equation is - 1 / 2.

Answer 2

16) x ^ 2 - x = λ(2x-1)

x ^ 2 - x = 2xλ -1λ

x ^ 2 - x - 2xλ + λ = 0

x^ 2 -(2λ +1) x + = 0

Sum of roots

2λ + 1 = 0

2λ= - 1

λ= - 1/2