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Find the value or values of p in the quadratic equation p^2+13p-30=0\r
\n" ); document.write( "\n" ); document.write( "p^2+13p-30=0 ----(1)
\n" ); document.write( "p^2 + [(15)p+(-2)p] - 30 =0
\n" ); document.write( "(splitting the middle term as the sum of two terms in such a way that these two when multiplied(of course along with the signs)should give the product of the square term and the constant term.)
\n" ); document.write( "That is [13p =(15)p+(-2)p] and (15p)X(-2p) = -30p^2= (p^2)X(-30)]
\n" ); document.write( "p^2 + 15p-2p -30= 0
\n" ); document.write( "p(p+15)-2(p+15)=0
\n" ); document.write( "pt-2t=0 where t= p+15
\n" ); document.write( "t(p-2)=0
\n" ); document.write( "(p+15)(p-2)=0
\n" ); document.write( "(p+15) = 0 gives p= -15
\n" ); document.write( "(p-2)=0 gives p= 2
\n" ); document.write( "Answer: p= -15 and p =2
\n" ); document.write( "Verification: p= -15 in p^2+13p-30=0 ----(1)
\n" ); document.write( "LHS=(-15)^2 +13X(-15)-30 = 225-195-30=0 =RHs
\n" ); document.write( "And p= 2 in p^2+13p-30=0 ----(1)
\n" ); document.write( "LHS=(2)^2 +13X(2)-30 = 4+26-30= 0 =RHs
\n" ); document.write( "Therefore our values are correct.\r
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