1)if a+b+c=0 then the equation 3ax^2 +2bx+c has in the interval(0,1)

a at least one root       b at the most one root      c no root          d none of these

2)if 27a+9b+3c+d=0   then the equation  4ax^3+3bx^2+2cx+d=0 has at least one root lying b/w

a  0 and 1        b 1and3        c 0and 3                    dnone of these

plz ans as soon as possible!!!!

rates for proper exp

only using that i get:

if f(0)>0 v get f(2/3)<0 n vice versa

if f(1/3)>0 then f(1)<0 n vice versa

2)

consider the eqn:

g(x)=ax^4 + bx^3 + cx^2 +dx +e

here g'(x)=eqn u mentioned in the question

g(0)=e

g(3) also =e

so g(0)=g(3)

hence from rolles theorem there exists values of x (0,3) such tht g'(x)=0

these values may be 1 or more

hence the answer is atleast 1 root in (0,3)

1)consider g(x)=ax^3 + bx^2 + cx +d

g(0)=d

g(1)=a+b+c+d=d(as a+b+c=0)

g(0)=g(1)...from rolles theorem there exist atleast 1 value in (0,1) such tht g'(x)=0

note tht g'(x) = the eqn u have given

hence ans is ---atleast 1 root