The number of values of the pair (a, b ) for which the equation α(x+1)2+β(x2−3x−2)+x+1=0,∀x∈R is identity

The equation α(x+1)2+β(x2−3x−2)+x+1=0,∀x∈Ris an identify in x ifα+β=0---i2α−3β+1=0----iiα−2β+1=0---iiiSolving Eq. (1) and (2), we get α=−15andβ=15But these values do not satisfy Eq. (3). Hence the given equation cannot be an identify for any values of αandβ