Practice Flashcards: Higher Maths: polynomials, quadratic theory and recurrence relations | Zestly

Question 1

Factor Theorem

Accepted Answer

If $f(a) = 0$, then $(x - a)$ is a factor of $f(x)$. Example: If $f(1) = 0$, then $(x - 1)$ is a factor.

Question 2

Remainder Theorem

Accepted Answer

The remainder when $f(x)$ is divided by $(x - a)$ is $f(a)$. Example: $f(x) = x^2 + 1$ divided by $(x - 2)$ leaves remainder $f(2) = 5$.

Question 3

Discriminant for equal roots

Accepted Answer

For $ax^2 + bx + c = 0$, equal roots occur when $b^2 - 4ac = 0$. Example: $x^2 + 4x + 4 = 0$ has $16 - 16 = 0$.

Question 4

Completing the square

Question 5

Recurrence relation limit

Question 6

Condition for recurrence convergence

Question 7

Repeated root on a graph

Question 8

Quadratic inequality solution

Question 9

Sum of roots

Question 10

Product of roots

Question 11

Synthetic division

Question 12

Turning point of $y = (x+p)^2 + q$