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Question

The quadratic equation whose roots are sin218 and cos236 is


A

16x2 - 12x + 1 = 0

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B

16x2 + 12x + 1 = 0

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C

16x2 - 12x - 1 = 0

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D

16x2 + 10x + 1 = 0

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Solution

The correct option is A

16x2 - 12x + 1 = 0


Since sin218 and cos236 are the roots of quadratic equation

sum of roots = sin218 + cos236

= (514)2 + (5+14)2 = 34

And products of roots = sin218.cos236

= (514)2.(5+14)2 = 116

Required equation whose roots are sin218 and cos236 is

x234x+116x=016x212x+1=0


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