Question

If Sinalpha is a root of 25x^2 + 5x - 12 = 0, -1 < x < 0

Then Cos2alpha = ?

a)" "0

b)" "7/25

c)-7/25

d)" "None

Solution

Given equation 25x^2 + 5x - 12 = 0

=> 25x^2 + 20x - 15x - 12 = 0

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

This will give

x = 3/5 and -4/5

Since given condition -1 < x < 0

Hence, taking negative value, x = Sinalpha = -4/5

Now we know that, Cos2alpha = 1 - 2Sin\^2 alpha

So, Cos2alpha = 1 - 2(-4/5)^2

=> Cos2alpha = 1 - 2(16/25) = (25-32)/25 = -7/25