document.write( "Question 451563: Solve the equation in the interval [0,2pi): 2 cos^2 theta + 3 cos theta + 1 = 0. \n" ); document.write( "

Algebra.Com's Answer #310516 by htmentor(1343) $\"\"$ $\"About$

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2 cos^2 theta + 3 cos theta + 1 = 0
\n" ); document.write( "To solve, let x = cos $\"theta\"$
\n" ); document.write( "So we have
\n" ); document.write( "2x^2 + 3x + 1 = 0
\n" ); document.write( "Solve using the quadratic formula:
\n" ); document.write( "x = (-3 +- sqrt(9 - 8))/4
\n" ); document.write( "This gives x = -1/2, x = -1
\n" ); document.write( "So we need to find the values of $\"theta\"$ on the interval [0,2 $\"pi\"$ ) which satisfy
\n" ); document.write( "cos $\"theta\"$ = -1/2, -1
\n" ); document.write( "cos $\"pi\"$ = -1, one of the zeros is $\"pi\"$
\n" ); document.write( "cos(2 $\"pi\"$ /3) = cos(4 $\"pi\"$ /3) = -1/2
\n" ); document.write( "So the zeros are: $\"theta\"$ = (2/3) $\"pi\"$ , $\"pi\"$ ,(4/3) $\"pi\"$
\n" ); document.write( "The graph is below:
\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C5%2C-2%2C6%2C2%2A%28cos%28x%29%29%5E2%2B3%2Acos%28x%29%2B1%29\"$ \n" ); document.write( "

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