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-2x squared + 10x = 15
\n" ); document.write( "Multiplying by (-1),we have,
\n" ); document.write( "2x^2-10x=-15
\n" ); document.write( "2x^2-10x+15 = 0 ----(1)
\n" ); document.write( "x = {-(-10) + or minus sqrt[(-10)^2 - 4X(2)X(15)]}/[2X(2)]
\n" ); document.write( "[Using x =[(-b)+or minus sqrt(b^2-4ac)]/2a for the given equation:(ax^2+bx+c)=0]
\n" ); document.write( "x={10+or minus sqrt(100-120)}/4
\n" ); document.write( "x=(1/4)X[10+ or minus sqrt(-20)]
\n" ); document.write( "x=(1/4)X[10+ or minus (2isqrt(5))]
\n" ); document.write( "x=(1/2)X[5+ or minus isqrt(5)] (cancelling 2 in the nr and dr )
\n" ); document.write( "Therefore the values are
\n" ); document.write( "x=[5+ i sqrt(5)]/2 and x=[5 - i sqrt(5)]/2
\n" ); document.write( "[sqrt(-20)= sqrt(5X4Xi^2)=sqrt(5X2^2i^2)=2i(sqrt(5))]
\n" ); document.write( "Verification: x=[5+ i sqrt(5)]/2 in (1)
\n" ); document.write( "LHS = 2x^2-10x+15
\n" ); document.write( "=2X {[5+ i sqrt(5)]/2 }^2-10X{[5+ i sqrt(5)]/2} +15
\n" ); document.write( "=2X{25+5i^2+10isqrt(5)}/4 -25-5isqrt(5) +15
\n" ); document.write( "=(25/2)+5/2X(-1)+5isqrt(5)-25-5isqrt(5)+15
\n" ); document.write( "=25/2-5/2-25+15
\n" ); document.write( "=(20/2)-10
\n" ); document.write( "=10-10
\n" ); document.write( "=0
\n" ); document.write( "=RHS
\n" ); document.write( "Therefore the above value of x is correct.
\n" ); document.write( "Complex roots always occur in conjugate pairs.
\n" ); document.write( "Hence no need to check for the validity of the other value of x.
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