Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x2+6x−(a2+2a−8)=0
x2+6x−(a2+2a−8)=0
Solving the Q.E in x,we have
x=−b±√b2−4ac2
Discriminant, D=b2−4ac
D=62−4(−(a2+2a−8))
=36+4a2+8a−32=36+4a2+8a−32=4a2+8a+4=4(a+1)2>0,so solution exists
x=−b±√D2
x=−6±√4(a+1)22
x=−6±2(a+1)2
x=−3+a+1 or x=−3−a−1
x=a−2 or x=−a−4