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Question

If cosα is a root of the equation 25x2+5x12=0,1<x<0, then the value of sin2α is

A
1225
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B
1225
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C
2425
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D
2025
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Solution

The correct option is C 2425
25x2+5x12=0x=35,45

Now, if cosα=35 then sinα= 1(35)2=45

sin2α=2sinαcosα=23545=2425

Similarly, if cosα=45 then sinα= 1(45)2=35

sin2α=2sinαcosα=23545=2425

Therefore, Answer is 2425

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