document.write( "Question 143579This question is from textbook prentice hall algebra 1
\n" ); document.write( ": How do I solve? Use the dicriminant to determine whether the graph of each quadratic function intersects the x-axis in zero, one, or two points:\r
\n" ); document.write( "\n" ); document.write( "p=-3q^2+4q+2 \n" ); document.write( "

Algebra.Com's Answer #104493 by Earlsdon(6294) $\"\"$ $\"About$

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The discriminant of a quadratic equation ( $\"f%28x%29+=+ax%5E2%2Bbx%2Bc\"$ )is: $\"b%5E2-4ac\"$ which is the radicand (the contents under the radical sign) of the quadratic formula.
\n" ); document.write( "If the discriminant is negative, the function will have two complex conjugate solutions (roots) and the graph of the function never intersects the x-axis.
\n" ); document.write( "If the discriminant is zero, the function will have one real solution (a double root) which is really two identical solutions which means that the graph of the function will just touch, but not cross, the x-axis.
\n" ); document.write( "If the discriminant is positive, the function will have two real solutions and the graph will cross the x-axis at two points.
\n" ); document.write( "Let's look at your equation:
\n" ); document.write( " $\"p+=+-3q%5E2%2B4q%2B2\"$ Here, a = -3, b = 4, and c = 2
\n" ); document.write( "The disciminant, D, is:
\n" ); document.write( " $\"D+=+4%5E2-4%28-3%29%282%29\"$
\n" ); document.write( " $\"D+=+16%2B24\"$
\n" ); document.write( " $\"D+=+40\"$ It's positive so there are two real solutions (roots) and the graph crosses the x-axis at two points. \n" ); document.write( "

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