Home
Class 11
MATHS
If 1/ sqrt(alpha) and 1/sqrt(beta) are ...

If ` 1/ sqrt(alpha) and 1/sqrt(beta)` are the roots of equation `a x^2 + bx + 1 = 0`(`a!=0, (a,b in R)`), then the equation `x(x + b^3) + (a^3 - 3abx) = 0` has roots -

Text Solution

Verified by Experts

eqn is `ax^2 + bx +1 =0`
so,roots will be `1/sqrt alpha & 1/sqrt beta`
can be written in the form `1/sqrt alpha + 1/sqrt beta = -b/a`
`(sqrt alpha + sqrt beta)/(sqrt alpha * sqrt beta)= -b/a`
`=1/sqrt(alpha beta) = 1/a`
now, `x(x+b^3) + (a^3 - 3abx) = 0`
`x^2 + b^3x - 3abx+a^3 = 0`
`x^2 + x(b^3 - 3ab) + alpha^(3/2) beta^(3/2) = 0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If (1)/(sqrt(alpha)) and (1)/(sqrt(beta)) are the roots of the equation px^(2)+qx+1=0(p!=0,p,q in R) then the equation x(x+q^(3))+(p^(3)-3pqx)=0 has roots

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

If alpha and beta are the roots of equation x^2-4x+1=0 , find alpha^3+beta^3

If 2alpha and 3beta are the roots of the equation x^(2) + az +b = 0 , then find the equation whose roots are a,b .

If alpha and beta are the roots of the equation x ^(2) + 3x - 4 = 0 , then (1)/(alpha ) + (1)/(beta) is equal to

alpha and beta are the roots of the equation x^(2) - 3x + 5 = 0 , the equation whose roots are (1)/(alpha) and (1)/(beta) is: