if the roots of the equation 4B^2+AB-2= are of the form (k/k+1)+(k+1/k+2), then what is the value of A ? note-A means alfha and B means bita due to non availability of sign i write it as A and B.

Question

Solve in detail.roots of equation I.e- alpha,bits.

Answer 1

 

Sum of roots (the negative coefficient of the middle term)=

k/(k+1)+(k+1)/(k+2)=(k(k+2)+(k+1)^2)/((k+1)(k+2))=(k^2+2k+k^2+2k+1)/(k^2+3k+2)=(2k^2+4k+1)/(k^2+3k+2).

Product of roots (constant term)=k/(k+2).

If the constant term is -2 then k/(k+2)=-2, so k=-2k-4 and 3k=-4, so k=-4/3.

This impacts on the middle term: (32/9-16/3+1)/(16/9-4+2)=(32-48+9)/(16-36+18)=-7/(-2)=7/2.

the quadratic would be of the form x^2+7x/2-2=0=(x-4)(x-1/2) or (x-4)(2x+1)=0.

If the coefficient of x^2 is 4B^2, then 4B^2=1 and B=1/2; if AB=-7/2, then A=-7.