document.write( "Question 6535: What describes the number and type of roots of the equation 4x^3 - 6x^2 + 15x + 2= 0? \n" ); document.write( "
Algebra.Com's Answer #3574 by khwang(438)\"\" \"About 
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Let f(x) = 4x^3 - 6x^2 + 15x + 2= 0
\n" ); document.write( " f'(x) = 12x^2 - 12x + 15 = 3(4x^2 - 4x + 5)
\n" ); document.write( " By the quadratic formula, we that f'(x) has no real roots(since
\n" ); document.write( " b^2 - 4ac < 0)
\n" ); document.write( " This shows that the function has no critical values and hence
\n" ); document.write( " no relative extremas.
\n" ); document.write( " By Roll's Theorem if f(x) = 0 has three roots, then f'(x) = 0
\n" ); document.write( " will have two roots.
\n" ); document.write( " But f is a real polynomial of odd degree, f(x) = 0 must have a
\n" ); document.write( " real root. In fact f(0) = 2 >0 and f(-1) = -4 -6 -15+2 < 0.
\n" ); document.write( " So, there is a root between 0 and 1. While the other
\n" ); document.write( " two roots are conjugate complex numbers.\r
\n" ); document.write( "\n" ); document.write( " If you are not above calculus level, then it is very hard to
\n" ); document.write( " solve this question. {may use Cardan's formula]\r
\n" ); document.write( "\n" ); document.write( " Kenny\r
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