Question

find the value of alpha in the following (17th question)

Answer 1

Q17:   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

Answer 2

We know that, When roots are equal, Discriminant = 0

Hence b²-4ac=0

2( α - 12)²-4( α -12) (2) =0
Let s = α -12

(2s)²-4(s)*2=0

4s²-8s=0

s²=2s

s=2

Now,

s=2

α-12=2

α=14

Hence, Value of α is 14 if the equation (α-12)x ²+ 2( α-12) x + 2 =0 have equal roots.