Question

If α and β are zeroes, of polynomial, x²--2x--15. Then form of a quadratic polynomial whose zeroes are 2α and 2β. also tell solution to problem pls pls

Answer 1

   P(x) =  x² - 2 x - 15 
   if  α and  β are the solutions or zeros or roots of P(x),
         then  P(β) = P(α) = 0
  
  Also,   α + β = - coefficient of x term / coefficient of x² = 2
               α β = constant term / coefficient of x² = -15
 
Now,  we want a quadratic polynomial, whose roots are 2 α and  2β.
    =>  sum of the roots = 2α+2β = 2(α+β) = 2 * 2 = 4
   =>  product of the roots = 2α * 2β = 4 αβ = 4 * -15 = -60

    Polynomial = x² - (sum of roots) x + product of roots 
                        = x² - 4 x - 60