Question

For what value of m, the equation x^2 −mx+m+1=0 may have its roots in the ratio 2:3

Answer 1

Answer:

Let the roots be 2x and 3x

sum of roots=-b/a

5x =m

Product of roots=c/a

6x^2=m+1

m=6x^2-1

5x=6x^2-1

6x^2-5x-1=0

6x^2-6x+x-1=0

6x(x-1)+1(x-1)=0

(6x+1)(x-1)=0

x=1 or x=-1/6