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tmua.me Extreme Set B Paper 1 · Q13

Paper 1Algebra

The curve

y=x4−3x2+1y=x^4-3x^2+1

meets the xx-axis at four distinct points.

The gradients of the normals at these points are n1,n2,n3,n4n_1,n_2,n_3,n_4.

What is the value of

n12+n22+n32+n42 ?n_1^2+n_2^2+n_3^2+n_4^2\,?
A310\dfrac3{10}
B320\dfrac3{20}
C110\dfrac1{10}
D35\dfrac35
E32\dfrac32
F65\dfrac65

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