document.write( "Question 699249: When are the roots of X^2 + ax + b complex? What does the sketch look like? \n" ); document.write( "

Algebra.Com's Answer #431319 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "if you have $\"x%5E2+%2B+ax+%2B+b\"$ , compared to general form $\"ax%5E2%2Bbx%2Bc\"$ your $\"a=1\"$ , $\"b=a\"$ and $\"c=b\"$ \r
\n" ); document.write( "\n" ); document.write( "using quadratic formula you can find roots: \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "this part is discriminant, and if discriminant is less than zero, you will have complex roots\r
\n" ); document.write( "\n" ); document.write( "in your case discriminant is:\r
\n" ); document.write( "\n" ); document.write( " $\"+%28+a%5E2-4%2A1%2Ab+%29%2F%282%2A1%29+\"$ and if it is less than zero, you will have complex roots\r
\n" ); document.write( "\n" ); document.write( "Graph has no real roots, it has no $\"x-intercepts\"$ , if both roots are complex. \r
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