document.write( "Question 763902: if on root of the equation 2x^2-kx+64=0 is twice the other root, then find the value of k \n" ); document.write( "

Algebra.Com's Answer #465104 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the roots be $\"a\"$ and $\"a%2F2\"$ .
\n" ); document.write( "If we knew the coefficients and $\"a\"$ was a nice round number we may solve such an equation by factoring.
\n" ); document.write( "Even when the roots are ugly irrational numbers, a polynomial can be written in factored form if you know the zeros.
\n" ); document.write( "In this case, the factored equation would be
\n" ); document.write( " $\"2%28x-a%2F2%29%28x-a%29=0\"$ or $\"%282x-a%29%28x-a%29=0\"$
\n" ); document.write( "Re-multiplying, we get
\n" ); document.write( " $\"2x%5E2-3ax%2Ba%5E2=0\"$
\n" ); document.write( "If that equation is equivalent to $\"2x%5E2-kx%2B64=0\"$ (both with $\"2\"$ for a leading coefficient),
\n" ); document.write( "then the other copefficientsa are also the same, so
\n" ); document.write( " $\"a%5E2=64\"$ and $\"-3a+=+-k\"$ --> $\"3a=k\"$
\n" ); document.write( " $\"system%28a%5E2=64%2C3a=k%29\"$ --> $\"system%28a=8%2Cor%2Ca=-8%29\"$ --> $\"system%28k=24%2Cor%2Ck=-24%29\"$ \n" ); document.write( "

\n" );