Cos\Theta is a root of the equation 25x^{2}+5x-12=0,\:\:-1< x< 0, then the value of Sin2\theta is,

  • Option 1)

    \frac{24}{25}

  • Option 2)

    \frac{-12}{25}

  • Option 3)

    \frac{-28}{25}

  • Option 4)

    \frac{20}{25}

 

Answers (1)

As we learnt in concept

Roots of Quadratic Equation -

\alpha = \frac{-b+\sqrt{b^{2}-4ac}}{2a}

\beta = \frac{-b-\sqrt{b^{2}-4ac}}{2a}
 

 

- wherein

ax^{2}+bx+c= 0

is the equation

a,b,c\in R,\: \: a\neq 0

 

 25 x^{2}+5x-12 =0

cos \theta is the root of this equation

Roots of this equations are :

\frac{-5 \pm \sqrt{25+4*12*25}}{50}

=\frac{-5 \pm \sqrt{25*49}}{50}

=\frac{-5\pm 35}{50}

=\frac{3}{5}, \frac{-4}{5}

\cos \theta= \frac{3}{5}\: \: , \sin \theta = \frac{4}{5}

Thus , \sin \2\theta= 2 \sin \theta \cos \theta

= 2*\frac{3}{5}*\frac{4}{5}

=\frac{24}{25}

 


Option 1)

\frac{24}{25}

Correct option

Option 2)

\frac{-12}{25}

Incorrect option 

Option 3)

\frac{-28}{25}

Incorrect option 

Option 4)

\frac{20}{25}

Incorrect option 

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