Which of the following is not the correct quadratic equation? If $3/2$ and $4$ are the two roots of a quadratic equation, then which one of the following is not the correct quadratic equation?
(A) $2x^2-11x+6=0$,
(B) $6x^2-33x+18=0$,
(C) $-10x^2-55x-30=0$,
(D) $4x^2-41x+24=0$.
I tried using the analogy $(x-3/2)(x-4)$ but it came to be of no use. My textbook tells me to interpret this as $k(x-3/2)(x-4)$. The equation comes out to have a constant ($c$ term) $+12$. However the options tell a different story altogether. A slight advice about the same will be most welcome.

Your textbook is suggesting a uselessly complicated method.
The sum of the roots is $11/2$ and their product is $6$. Dividing by the leading coefficient should make the equation in the form
$$
x^2-\dfrac{11}{2}x+6=0
$$
and the form of this equation is unique. Now we have
(A) $x^2-\dfrac{11}{2}x+3=0$ (divide by $2$)
(B) $x^2-\dfrac{11}{2}x+3=0$ (divide by $6$)
(C) $x^2-\dfrac{11}{2}x+3=0$ (divide by $-10$)
(D) $x^2-\dfrac{41}{4}x+6=0$ (divide by $4$)
So the answer is that none of the proposed equations has roots $3/2$ and $4$.
