If (x - 2) and (x + 3) are the factors of the equation $$x^{2} + k_1x + k_2 = 0$$, then what are the values of $$k_1$$ and $$k_2$$ ?

Equation : $$f(x)=x^{2} + k_1x + k_2 = 0$$

If $$(x-2)$$ and $$(x+3)$$ are factors of above equation, then $$x=2,-3$$ will satisfy above equation.

=> $$f(2)=(2)^2+k_1(2)+k_2=0$$

=> $$2k_1+k_2=-4$$ ----------(i)

Similarly, $$f(-3)=(-3)^2+k_1(-3)+k_2=0$$

=> $$-3k_1+k_2=-9$$ ----------(ii)

Subtracting equation (ii) from (i), we get :

=> $$5k_1=-4+9=5$$

=> $$k_1=\frac{5}{5}=1$$

Substituting it in equation (i), => $$k_2=-4-2(1)=-4-2=-6$$

=> Ans - (B)