# SPM Questions for Quadratic Equations

We will discuss some pass year SPM exam questions based on:

• Solve the quadratic equations – SPM 2003, SPM 2005
• Form a quadratic equation – SPM 2009
• Determine the conditions for the type of roots – SPM2010

### Solve the quadratic equations – SPM 2003 Paper 1 Question 3

(3 marks)

Note: If you have any doubt, please refer back my previous post on how to solve the equation using completing the square method.

(3 marks)

### Form a quadratic equation – SPM 2009 Paper 2 Question 2

The quadratic equation x2 – 5x + 6 = 0 has roots h and k, where h > k.

(a) Find

i) the value of h and of k.
ii) the range of x if x2 – 5x + 6 > 0
(5 marks)

(b) Using the values of h and k from 2(a)(i), form the quadratic equation which has roots h + 2 and 3k – 2.
(2 marks)

a i) For x– 5x + 6 = 0, given roots are h and k,

ii)

(b)

$h + 2$
$= 3 + 2$
$= 5$

$3k - 2$
$= 3(2) - 2$
$= 4$

$SOR = 5 + 4 = 9$
$\text{POR = 5 x 4 = 20}$

$Equations:$
${{x}^{2}}-(\text{SOR)}x+(\text{POR)}=0$
$\underline{{{x}^{2}}-9x+20=0}$

### Determine the conditions for the type of roots – SPM 2010 Paper1 Question 5

The quadratic equation (1-p)x2 – 6x +10 = 0, where p is a constant, has two different roots. Find the range of values of p.

(3 marks)