document.write( "Question 135205: calculate the value of the discriminant of x^ + 2x +1 = 0 by examining the sign of the discriminant in part a, how many x- intercepts would the graph of y + x^ + 2x +1 have ? Why? \n" ); document.write( "

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The discriminant of $\"ax%5E2%2Bbx%2Bc=0\"$ is $\"+b%5E2-4%2Aa%2Ac+\"$ . For your equation, a = 1, b = 2, and c =1.\r
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\n" ); document.write( "\n" ); document.write( "If the discriminant is >0 (positive), then there are two different real roots to the equation. Graphically this means that the graph of the function $\"y=ax%5E2%2Bbx%2Bc\"$ will intersect the x axis in two different points.\r
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\n" ); document.write( "\n" ); document.write( "If the discriminant = 0, then there are two real and identical roots (or one real root with a multiplicity of two). Graphically, this means that the curve is tangent to the x-axis at the vertex of the parabola and there is one point of intersection, or one x-intercept.\r
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\n" ); document.write( "\n" ); document.write( "If the discriminant <0, (negative), then there are no real roots, although there is a conjugate pair of complex roots involving the imaginary number i where i is defined as $\"i%5E2=-1\"$ . Graphically, the curve will have no points of intersection with the x-axis. \n" ); document.write( "

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