Answer:
n = 17
Explanation:
For a quadratic equation to have equal roots b²-4ac should be equal to zero in the quadratic equation ax²+bx+c=0.
Equation : 3x² - 12 x + ( n - 5) = 0
a = 3, b = -12, c = ( n - 5)
b² - 4ac = 0
(-12)² - (4 x 3 x (n - 5)) = 0
144 - 12( n - 5 ) = 0
12( n - 5 ) = 144
n - 5 = 12
n = 17
Check if it's true :
3x² - 12 x + ( 17 - 5) = 0
3x² - 12 x + 12 = 0
3(x² - 4x + 4) = 0
(x² - 4x + 4) = 0
(x - 2)(x - 2) = 0
x = 2 , 2
Equal roots .