document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18720>Question 18720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Okay, I really need an understanding on Quadratics. Could some one help me understand this problem?\r<BR>\n" );
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document.write( "The instructions are to: Use the discriminate to determine whether this quadratic polynomial can be factored, factor the numbe is it is not prime.<BR>\n" );
document.write( "8x^2 - 10x - 3\r<BR>\n" );
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document.write( "Thank you all for the help!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8976 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the discriminate to determine whether this quadratic polynomial can be factored, factor the numbe is it is not prime.<BR>\n" );
document.write( "8x^2 - 10x - 3\r<BR>\n" );
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document.write( "the roots or values of x which satisfy the following quadratic  equation ( called a solution for the eqn) ax^2+bx+c=0 is given by the formula <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..<BR>\n" );
document.write( "here we find the critical term which determines the nature of solution is the term under square root namely<BR>\n" );
document.write( "b^2-4ac which is called the discriminant (D in short)<BR>\n" );
document.write( "if D is -ve the square root becomes imaginary...then there are no roots.<BR>\n" );
document.write( "if D=0,we will have 2 equal roots or..the expression will be a perfect square.<BR>\n" );
document.write( "if D>0 and a perfect square .then we will have 2 distinct rational roots.<BR>\n" );
document.write( "if D>0 ,but not a perfect square we will have 2 distinct irrational roots <BR>\n" );
document.write( "here in your example we have D=(-10)^2-4*8*(-3)=100+96=196 which is positive and perfect square (14*14=196)..so it will have 2 distinct rational roots ..you can find them by using the above formula..once you find the 2 roots as say p and q then the given equation can be factored and written as {EQUIVALENT} to <BR>\n" );
document.write( "(x-p)*(x-q)=0...in the above example we get p=3/2 and q=-1/4...so<BR>\n" );
document.write( "8x^2-10x-3=0 is EQUIVALENT to (x-3/2)(x+1/4)=0...NOTE THAT THE TWO EXPRESSIONS GIVEN BY 8x^2-10x-3 and (x-3/2)(x+1/4) are not same but theeir equations with zero {8x^2-10x-3=0 and (x-3/2)(x+1/4)=0.}gives the same solution set of <BR>\n" );
document.write( "x=3/2 or -1/4..hence they are called equivalent but not same expression.if you want the same expression you have to find a constant say k which when multiplied with gives same expressions .here we find that k=8 since <BR>\n" );
document.write( "8x^2-10x-3=8(x-3/2)(x+1/4)=4*2(x-3/2)(x+1/4)=2(x-3/2)*4(x+1/4)=(2x-3)(4x+1)=<BR>\n" );
document.write( "8x^2-10x-3 </SPAN>\n" );
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