2010 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
x^2 -6x + 34 = 0

x = \frac{6 \pm \sqrt{36-136}}{2}

x = 3 \pm 5i

(ii)
Since the coefficients are all real, another root of the equation is -2-i

[x-(-2+i)][x-(-2-i)]

= x^2 + 4x +5

By comparing coefficients,

x^4 + 4x^3 + x^2 + ax + b = (x^2+4x+5)(x^2-4)

\therefore, a=-16, b = -20

The other three roots are -2 - i, 2, -2

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