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Question

If sin α and cos α are the roots of the equation ax2+bx+c=0, then

A

a2 - b2 + 2ac = 0

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B

(a - c)2 = b2 + c2

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C

a2 + b2 + 2ac = 0

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D

(a - c)2 = b2 - c2

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Solution

The correct option is A

a2 - b2 + 2ac = 0


Sum of the roots = ba
Product of the roots = ba
sin α+cos α=ba.......(1)sin α×cos α=ca.......(2)Squaring(1) gives(sin α+cos α)2=(ba)2(sin α)2+(cos α)2+2 sin α×cos α=(ba)21+2×(ca)=(ba)2Multiplying with a2 gaves a2+2ac=b2a2b2+2ac=0


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