Chapter 2 · Question 4

Find the zeroes of $x^2-5x+6$ and verify the coefficient relations.

Answer

Factorise:

x^2-5x+6=(x-2)(x-3)

. Zeroes are

2

and

3

. Sum

=5=-\frac{-5}{1}

and product

=6=\frac61

.

The zeroes are

2

and

3

. Their sum is

5

and product is

6

, matching the formula.

Factorise the polynomial:

x^2-5x+6=(x-2)(x-3)

. Hence the zeroes are

2

and

3

. For

a=1,b=-5,c=6

,

-\frac ba=-\frac{-5}{1}=5

, which equals

2+3

. Also

\frac ca=\frac61=6

, which equals

2\times3

. Thus the relation is verified.