Bs Grewal solutions: SOLVE THE EQUATION 6X^3-11X^2-3X+2=0 Given roots are in H.P

QUESTION:-SOLVE THE EQUATION 6X^3-11X^2-3X+2=0 Given roots are in H.P

SOLUTION:-

GIVEN THAT THE EQUATION OF THE ARE IN HP, THE ROOTS OF THE EQUATION HAVING RECIPROCAL ROOTS WILL BE IN A.P.

THE EQUATION WITH RECIPROCAL ROOTS IS

6(1/X)^3-11(1/X)^2-3(1/X)+2=0

2X^3-3X^2-11X+6=0 ---------1 EQUATION

SINCE THE ROOTS OF THE EQUATION ARE IN HP, THEREFORE THE ROOTS OF EQUATION 1 IS IN AP. LET THE ROOTS BE a-d, a+d then

By adding these roots we get,

3a=3/2

a=1/2

and by multiplying we get

a(a^2-d^2)=-3

½(1/4d^2)=-3

¼-d^2=-6

¼+6=25/4

d=5/2

thus, the roots of equation 1 are -2,1/2,3

Hence the roots of the given equation are -1/2,2,1/3

Bs Grewal solutions