If x=-1 and x=2 are extreme points of $\;f(x) =\alpha log|x|+ \beta x^{2}+x\;$ then :

Question

$(a)\;\alpha=2 ,\beta=-\large\frac{1}{2}\qquad(b)\;\alpha=2 ,\beta=\large\frac{1}{2}\qquad(c)\;\alpha=-6 ,\beta=\large\frac{1}{2}\qquad(d)\;\alpha=-6 ,\beta=-\large\frac{1}{2}$