If the sum of the roots of the equations x to the power 2-x=lambda(2x-1) is zero then lambda=
Answers
Answer:
λ = -1/2
Step-by-step explanation:
We are given that
x² - x = λ(2x - 1)
By shifting all the terms to left side we get
x² - x - λ(2x - 1) = 0
x² - x - λ2x + λ = 0
x² - x(1 + 2λ) + λ = 0
By comparing it with
ax² + bx + c = 0
we get
a = 1 , b = -(1 + 2λ) and c = λ
Now
We know that
Sum of roots = -b/a
Putting the value we get
Sum of roots = (1 + 2λ) / 1 = (1 + 2λ) .....(1)
But according to given condition
Sum of roots = 0 .....(2)
So
By comparing equation (1) and (2)we get
2λ + 1 = 0
⇒ 2λ = -1
⇒ λ = -1/2
Hence
λ = -1/2
Answer:
Lamda= -1/2
Explanation
we are given that ,
x²-x=lambda (2x-1)
BY SHIFTING ALL THE TERMS TO ONE SIDE WE GET
x²-x‐lamda(2x-1)=0
x²-x-lambda2x + lambda = 0
x²-x(1+2lambda)+ lambda = 0
BY COMPARING IT WITH
ax²+bx+c = 0
we get
a = 1 , b = -(1+2lambda) and c = lambda
now we know that
SUM OF ROOTS =-b/a
putting the value we get
SUM OF ROOTS =(1+2lambda) / 1 = (1 + 2 lambda)..........(i)
but according to the given condition
Sum of roots = 0.........(ii)
so
by comparing (i) and (ii) we get ,
2 lambda + 1 = 0
2 lambda = -1
LAMBDA = -1/2
HENCE LAMBDA = -1/2
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