Given that the question 2x^2+x-4 has roots a and B, form a quadratic equation with integer coefficients and with roots (a-(1/2B)) and (B-(1/2a))

a+B= -1/2
aB=2

Question

Given that the question 2x^2+x-4 has roots a and B, form a quadratic equation with integer coefficients and with roots (a-(1/2B)) and (B-(1/2a))

a+B= -1/2
aB=2

anonymous · Answer

i don't understand... what's the quesion?

anonymous · Answer

$$
a-\frac{1}{2}B=\frac{2a-B}{2}=r_1\
B-\frac{1}{2}a=\frac{2B-a}{2}=r_2
$$
$$r_1+r_2=\frac{a-B}{2}\
r_1r_2=\frac{(2a-B)(2B-a)}{4}$$

$$P(x)=(x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2$$
$$
\begin{align}
P'(x)&=x^2+\frac{B-a}{2}x+\frac{(2a-B)(2B-a)}{4}\
&=4x^2+2(B-a)x+(2a-B)(2B-a)
\end{align}$$

This doesn't get anymore fun... Solve from here.

anonymous · Answer

From the original equation, we have that the sum of the roots is -1/2, and the product of the roots is -2, not positive 2.

anonymous · Answer

Hi the product of roots is positive 2 as i have accidentally wrote the wrong equation it is  2x^2+x+4:D Thank yiu

anonymous · Answer

May I ask why you removed my medal? It is not the goal of this site to give complete answers.