Symbiosis National Aptitude Test SNAP 2017 Paper

Let a be a common root of the two given equation, then
${\mathit{\alpha }}^2-3\mathit{a}\mathit{\alpha }$ + 35 = 0 and ${\mathit{\alpha }}^2-\mathit{a}\mathit{\alpha }$ - 21 = 0
On subtracting we get -2aα + 56 = 0
or α = $\frac{28}{\mathit{\alpha }}$
as α is a root of ${\mathit{x}}^2$ - ax - 21 = 0
∴ ${\left(\frac{28}{\mathit{a}}\right)}^2-\mathit{a}\left(\frac{28}{\mathit{a}}\right)-21$ = 0
or ${\mathit{a}}^2$ = $4^2$ or a = ± 4