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 9 How to solve this recurrence relation? $f_n = 3f_{n-1} + 12(-1)^n$ 3 Confusion about covariance 2 If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$, then prove that $P(x) \cdot Q(x) = 0$ has at least two real roots? 1 Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$ 1 Adjusting mean and standard deviation

### Reputation (320)

 +105 How to solve this recurrence relation? $f_n = 3f_{n-1} + 12(-1)^n$ +20 If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$, then prove that $P(x) \cdot Q(x) = 0$ has at least two real roots? +25 Calculating Variance of a binomial distribution using the standard formula $E(X^2) - \mu^2$ +10 Confusion about covariance

### Questions (2)

 1 Can two functions have identical first and second derivatives, but different higher order derivatives? 1 Help Needed: Partial Derivative Identity/Chain Rule

### Tags (17)

 9 linear-algebra 3 random-variables 9 recurrence-relations 2 quadratic-equation 9 recursive-algorithms 2 quadratics 5 probability × 4 2 algebra-precalculus 4 statistics × 3 1 correlation

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