2001 HKCEE Maths MC Q39

This one is out of syllabus in CE maths, but not out of syllabus in CE a.maths.

Consider the quadratic equation x^2 + 4x + 1 = 0

Since x = a, x = b satisfy the equation

So, x = a, x = b are the roots of x^2 + 4x + 1 = 0

Hence, sum of roots, a + b = -4

Product of roots, ab = 1



Method 1:

a^2 + b^2

= a^2 + 2ab + b^2 - 2ab

= (a + b)^2 - 2ab

= (-4)^2 - 2(1)

= 14


Method 2:

From the given information,

a^2 = -4a - 1 and b^2 = -4b - 1

So, a^2 + b^2

= (-4a - 1) + (-4b - 1)

= -4(a + b) - 2

= -4(-4) - 2

= 14

Hence, the answer is C.