Core Chapter 2: Equations

Question 1

Solve equations of the form x²=k

Answer 1

1) When k>0, x=±√k
2) When k=0 , x=0
3) When k<0, there are no real solutions for x
4) When equation is in the form (x+a)²=k, solve as x²=k

Question 2

Solve power equations (xⁿ=k) when n are both even and odd powers

Answer 2

x=n√k
- If n is even (even power), there will be 2 answers
- If n is odd (odd power), there will only be 1 answer

Question 3

Apply the null factor law to factorise equations

Answer 3

Null factor law: if the product of 2 or more numbers is 0, then at least 1 of them must be 0

Question 4

What is a quadratic equation and how can quadratic equations be solved?

Answer 4

Quadratic equation: Polynomial equation with a degree of 2, can be expressed in the form y=ax²+bx+c, where a≠0, and can have 2/1/0 solutions

1) Factorisation
(apply null factor law)
2) Completing the square*
[and solve as (x+a)² =k]
3) Quadratic formula
(x= [-b ± √(b² - 4ac)]/2a
4) GDC
(Graphing: Menu –> 6 –> 1)

Question 5

Find discriminant to determine the number of solutions to a quadratic equation

Answer 5

Discriminant (Δ):
Δ = b²-4ac

Δ >0: 2 solutions
Δ =0: 1 solution)
Δ <0: 0 solutions