Question

If roots of equation x3-9x2+14x+24=0 are in ratio 3:2

Answer 1

it is very clear from the cubic equation f(x)

f(-1)=0,hence -1 is one of the root

as the other roots are in 3:2 ratio ,the roots will be 3a,2a,-1.

sum of the roots =-b/a=9

3a+2a+-1=9

5a=10

a=2

hence the roots are 6,4,-1