# If a and b are the roots of the equation 2x^2−px+7=0 Then a-b is a root of ?

If a and b are the roots of the equation
$2{x}^{2}-px+7=0$
Then a-b is a root of ?
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So, $a+b=\frac{p}{2}$ and $ab=\frac{7}{2}$
If $y=a-b=>{y}^{2}=\left(a+b{\right)}^{2}-4ab$
$=>{y}^{2}=\left(\frac{p}{2}{\right)}^{2}-4\frac{7}{2}$
So, a-b is a root of $4{y}^{2}-{p}^{2}+56=0$