Home
Class 11
MATHS
Let alpha,beta be the roots of the equat...

Let `alpha,beta` be the roots of the equation `(x-a)(x-b)=c ,c!=0.` Then the roots of the equation `(x-alpha)(x-beta)+c=0` are `a , c` b. `b , c` c. `a , b` d. `a+c , b+c`

Text Solution

Verified by Experts

Since `alpha, beta` are the roots fo
`(x-a)(x-b)=c`
or `(x-a)(x-b)-c=0`
Then `(x-a)(x-b)-c-(x-alpha)(x-beta)`
`implies(x-alpha)(x-beta)+c=(x-a)(x-b)`
Hence roots of `(x-alpha)(x-beta)+c=0` are a,b.
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are - (alpha+1//beta)and-(beta+1//alpha) .

If a

If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 then find the equation whose roots are (alpha + beta)^2 and (alpha-beta)^2

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0