Home
Class 12
MATHS
If alpha and beta are the complex roots ...

If `alpha` and `beta` are the complex roots of the equation `(1+i)x^(2)+(1-i)x-2i=o` where `i=sqrt(-1)`, the value of `|alpha-beta|^(2)` is

Text Solution

Verified by Experts

The correct Answer is:
5
`:'(1+i)x^(2)+(1-i)x-2i=0`
`impliesx^(2)+((1-i))/((1+i))x-(2i)/((1+i))=0`
`impliesx^(2)-ix-(1+i)=0`
`:. alpha +beta=i` and `alpha beta =-(1+i)`
`:.alpha -beta=sqrt((alpha +beta)^(2)-4alpha beta)=sqrt(i^(2)+4(1+i))=sqrt((3+4i))`
`|alpha-beta|=sqrt(sqrt(9+16))=sqrt(5)`
`:.|alpha-beta|^(2)=5`
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha and beta are the root of the equation x^(2)-x+1=0 then alpha^(2009)+beta^(2009)=

If alpha , beta are the roots of the equation : x^(2) + x sqrt(alpha) + beta = 0 , then the values of alpha and beta are :

If alpha and beta are the roots of the equation x^(2) - p(x + 1) - q = 0 , then the value of : (alpha^(2) + 2 alpha + 1)/(alpha^(2)+ 2 alpha + q) + (beta^(2) + 2 beta + 1)/(beta^(2) + 2 beta + q) is :

If alpha and beta are roots of the equation x^(2) + x + 1 = 0, then alpha^(2) + beta^(2) is

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If alpha and beta are the roots of x^(2)+x+1=0 , then alpha^(16)+beta^(16)=

If alpha and beta are the zeroes of the quadratic polynomial 2-3x-x^(2) then what is the value of alpha+beta+alpha beta ?

If alpha and beta be the roots of the equation x^(2) + 7x + 12 = 0 . Then equation whose roots are (alpha + beta)^(2) and (alpha - beta)^(2) is :

If alpha and beta are the roots of the equation 2x^2-3x + 4=0 , then the equation whose roots are alpha^2 and beta^2, is

If alpha and beta be the two zeroes of the quadratic polynomial p(x) = 2x^(2) - 3x + 7 , evaluate . i] alpha^(3) + beta^(3) ii] (1)/(2 alpha - 3) + (1)/( 2 beta - 3)