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Question

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

A
24/25
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B
12/25
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C
12/25
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D
20/25
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Solution

The correct option is A 24/25
Rewriting the equation ;

25x2+20x15x+12=0

5x(5x+4)3(5x+4)=0

(5x+4)(5x3)=0

x=45orx=35

As x>0 x=4/5= cosα

sinα=3/5

sin2α=2sinαcosα

sin2α=2×3/5×4/5

sin2α=24/25

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