Question

if x=_2 and x=3 are the solutions of the quadratic equation 3x square-2kx+2m=0.Find the value of k and m

Answer 1

Adding to the answers already given , this problem is solved with the help of a CAS such as Mathematica by typing the following code :

sol = Solve[3 x^2 - 2 k x + 2 m == 0, x];
Solve[2 == sol[[1, 1, 2]] && 3 == sol[[2, 1, 2]], {k, m}]

The result or answer obtained is :

k=152k=152 and m=9m=9 .

For a more general equation of the form

ax2+bkx+cm=0ax2+bkx+cm=0 with roots x1x1 and x2x2 ,

the solution is :

k=−a(x1+x2)bk=−a(x1+x2)b and m=ax1x2cm=ax1x2c .