document.write( "Question 1047203: Use the discriminant to determine whether the following equations have real solutions:0.0134x² + 0.0414 x + 0.0304 = 0 \n" ); document.write( "

Algebra.Com's Answer #662724 by KMST(5328) $\"\"$ $\"About$

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An equation of the form $\"ax%5E2%2Bbx%2Bc=0\"$ ,
\n" ); document.write( "with real numbers $\"a\"$ , $\"b\"$ , and $\"c\"$ ,
\n" ); document.write( "where $\"a%3C%3E0\"$ is called a quadratic equation.
\n" ); document.write( " $\"0.0134x%5E2+%2B+0.0414+x+%2B+0.0304+=+0\"$ is a quadratic equation.
\n" ); document.write( "There is a formula to find the solutions to a quadratic equation, called 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( "The expression $\"b%5E2-4%2Aa%2Ac\"$ that is under the square root is called the determinant.
\n" ); document.write( "The result of the quadratic formula is one or two real numbers if and only if
\n" ); document.write( "the determinant is not negative:
\n" ); document.write( " $\"b%5E2-4%2Aa%2Ac%3E=0\"$ .
\n" ); document.write( "(If $\"b%5E2-4%2Aa%2Ac=0\"$ there is only one solution; if $\"b%5E2-4%2Aa%2Ac%3E0\"$ there are two different real solutions).
\n" ); document.write( "In the case of the quadratic equation $\"0.0134x%5E2+%2B+0.0414+x+%2B+0.0304+=+0\"$ ,
\n" ); document.write( " $\"a=0.0134\"$ ,
\n" ); document.write( " $\"b=0.0414\"$ , and
\n" ); document.write( " $\"c=+0.0304+\"$ , so
\n" ); document.write( " $\"b%5E2-4%2Aa%2Ac+=+0.0414%5E2-4%2A0.0134%2A0.0304+=+0.00171396+-+0.0162944=0.00008452%3E0\"$ ,
\n" ); document.write( "so there will be 2 real solutions. \n" ); document.write( "

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