Question

find the value of alpha for which the quadratic equations (alpha -12)x square +2(alpha-12)x+2=0 has equal roots hence find the roots of equation

Answer 1

Hope it may help you...

Answer 2

Answer:

Given quadratic equation in x:

      

   (α - 12) x² + 2 (α - 12) x + 2 = 0

         Let  α - 12 = a.

 So   a x² + 2 a x + 2 = 0

        Discriminant = (2a)² - 4 * a * 2 = 4a² - 8 a

If the roots are real and equal, then the discriminant must be zero.

     So  4a² - 8 a = 0     =>  a = 2.

  Hence   α - 12 = 2    =>   α = 14