Q. In the equation x 2 + a x - a 2 - 1 = 0 has roots of opposite signs, then determine the interval in which 'a' lies. Share with your friends Share 1 Neha Sethi answered this Dear student We havex2+ax-a2-1=0Given: Roots of the equation are of opposite signs.⇒The product of roots will be negative.Also, product of roots=constant termcoeff. of x2=-1+a21 =-1+a2So, Product will be less than 0⇒-1+a2<0⇒1+a2>0⇒a2>-1 for real a, a2is always positive which is satisfied by above.So a can be any real number ranging from -∞ to +∞So, a lies in -∞,∞ Regards -1 View Full Answer