document.write( "Question 369498: Find the largest value of k such that the roots of the equation 2x^2+5x+k=0 are real. \n" ); document.write( "
Algebra.Com's Answer #263321 by CharlesG2(834)\"\" \"About 
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Find the largest value of k such that the roots of the equation 2x^2+5x+k=0 are real. \r
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\n" ); document.write( "\n" ); document.write( "2x^2 + 5x + k = 0
\n" ); document.write( "this is of form ax^2 + bx + c = 0,
\n" ); document.write( "which is a quadratic equation,
\n" ); document.write( "a = 2, b = 5, c = k
\n" ); document.write( "use the discriminant b^2 - 4ac from the quadratic formula
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "b^2 - 4ac = 5^2 - 4(2)k = 25 - 8k
\n" ); document.write( "the disciminant needs to be greater than or equal to 0 for there
\n" ); document.write( "to be real roots
\n" ); document.write( "25 - 8k >= 0
\n" ); document.write( "-8k >= -25
\n" ); document.write( "8k <= 25 (flipped sign since divided by negative)
\n" ); document.write( "k <= 25/8
\n" ); document.write( "k <= 3 1/8
\n" ); document.write( "k <= 3.125
\n" ); document.write( "the largest k such that the roots are real is 25/8 or 3.125
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