Question

If alpha and beta are the are zeros of polynomial x^{2} -2x-15 then form a quadratic polynomial whose zeros are 2alpha and 2beta

Answer 1

$x^2-2x-15=0$
Simply replace $x$ by $\frac{x}{2}$ to get an equation whose roots are $2$ times the roots of above equation :
$\left(\frac{x}{2}\right)^2-2\left(\frac{x}{2}\right)-15=0$
$\frac{x^2}{4}-x-15=0$
$x^2-4x-60=0$

Answer 2

  P(x)  =  x² - 2 x - 15  = 0    has solutions (roots) : α and β.
   Sum of roots = - coefficient of x: =>   α + β = 2
   product of roots = constant term  =>   α β = - 15

     then 2α + 2β = 4      and  2α * 2β  = -15 * 4 = - 60

quadratic polynomial :  x² - (sum of roots) x + product of roots.
  The quadratic polynomial :  x² - 4 x - 60