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A hint to get started

Recast a quartic as a rational-curve intersection

C:y=(x2+3x+1)/(2x−1)C:y=(x^2+3x+1)/(2x-1).

(i) Sketch C with axial intercepts, asymptotes and stationary points. marks

(ii) Add a suitable curve to deduce how many real roots 2x4+6x3+2x2+2x−1=02x^4+6x^3+2x^2+2x-1=0 has. marks

[2013/CJC/CA1/2]

CJC · Review problems · Question 2

Choose the comparison curve by rearranging the polynomial into the given rational function.

Read the worked solution