Home
Class 12
MATHS
If alpha,beta are the roots of the equat...

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`

Text Solution

Verified by Experts

`:'ax^(2)-bx(x-1)+c(x-1)^(2)=0`……….i
`impliesa(x/(x-1))^(2)-b(x/(x-1))+c=0`
or `a(x/(1-x))^(2)+b(x/(1-x))+c=0`
Now `alpha, beta` are the roots of `ax^(2)+bx+c=0`
Then `alpha=x/(1-x)` and `beta=x/(1-x)`
`impliesx=(alpha)/(alpha+1)` and `x=(beta)/(beta+1)`
hence `(alpha)/(alpha+1),(beta)/(beta+1)`,are the roots of the Eq. (i).
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the roots of the equation 2x^(2) + 10 x + 20 =0

Roots of the equation x^(2) -2x+ 1 =0 are :

Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is

If alpha, beta are the roots of the equation x^(2)-2x-a^(2)+1=0 and gamma, delta are the roots of the equation x^(2)-2(a+1)x+a(a-1)=0 such that alpha, beta epsilonn (gamma, delta) find the value of a .

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

Let alpha, beta the roots of the equation (x - a) (x - b) = c , c ne 0. Then the roots of the equation (x - alpha ) x - beta) + c = 0 are :

If alpha, beta be the roots of the equation x^2-px+q=0 then find the equation whose roots are q/(p-alpha) and q/(p-beta)

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