Question

If λ ? R is such that the sum of the cubes of the roots of the equation, x2+(2−λ)x +(10−λ)=0 is minimum, then the magnitude of the difference of the roots of this equation is meritnarion

Answer 1

Answer:

no idea

Step-by-step explanation:

Answer 2

SOLUTION :  

Option (c) is correct : - 1/2

Given : x² - x = λ(2x - 1) and sum of roots is zero.

x² - x = λ(2x - 1)

x² - x = 2λx - λ

x² - x -  2λx +  λ = 0

x² - (1 +  2λ)x +  λ = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 1 , b = - (1 +  2λ) , c =  λ

Sum of roots = - b/a

Sum of roots = - - (1 +  2λ) /1

Sum of roots = (1 +  2λ)/1

0 = (1 +  2λ)/1

[Given : Sum of roots = 0 ]

(1 +  2λ) = 0

2λ = - 1

λ = - 1/2

Hence, the value of λ is - ½.

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