**Question**

The roots of the
quadratic equation 2
x^{2} – 3x + 6 = 0 are a and b.(i) Without finding
the value of a,
show that 8a^{4} = 18 – 45a.(ii) Find the quadratic
equation whose roots are (a^{2} + 1) and
(b ^{2} + 1). |

**Introduction**

Do you know what a “root” is? Is it like radish or ginseng? Do you know what “satisfied” means? Is it that nice feeling you get when you eat carrots? Read on!

The featured problem above is modified
from an original question that contained an error. The modified part is shown in red. I present two solutions. The first solution uses pretty much standard
theory, and I use notations

*a*’ and*b*’ to denote the new roots (*a*^{ 2}+ 1) and (*b*^{2}+ 1) respectively. For the second solution, I present an alternative working part (i), and one using the**for obtaining new equations (not usually taught in schools at the secondary level) for part (ii). But before that let me first explain what “root” and “satisfied” means.***method of substitution***Recapitulation of Standard Theory**

**Solution 1 – Using Standard Theory**

**Solution 2 – Using the Method of Substitution for part (ii)**

**Remarks**

Once again we can see that there are many
ways to skin the cat, as it were. Mathematics
is not about following a fixed procedure.
There are various truths, notions and rules that are inviolable. But other than that, you can have as much
creativity as you want!

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in another way

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* other syllabuses that involve quadratic
roots

* whoever loves roots and enjoy being
satisfied by conquering mathematical challenges J

## No comments:

## Post a Comment