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Question

If α and β are the roots of the quadratic equation ax2+bx+c=0, then limx α1cos(ax2+bx+c)(xα)2 is :

A
(αβ)22
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B
2(αβ)2
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C
2a2(αβ)2
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D
a2(αβ)22
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Solution

The correct option is D a2(αβ)22
ax2+bx+c=a(xα)(xβ)

limx α1cos(ax2+bx+c)(xα)2

=limx α1cos(a(xα)(xβ))(xα)2

=limx α2sin2(a(xα)(xβ)2)(xα)2

=limx α2sin2(a(xα)(xβ)2)a2(xα)2(xβ)222×a2×(xβ)24

=2×1×a2(αβ)24

=a2(αβ)22

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