Question

Question no 12 guys.....solve this​

Answer 1

Answer:

α = 14 or 12

Step-by-step explanation:

Given that the equation has equal roots

so, the determinant of the equation = 0   i.e Δ = 0

=> b² - 4ac = 0

now, consider the equation, (α - 12)x² + 2(α - 12)x + 2 = 0

from the equation we get, b = 2(α - 12)

a = (α - 12) ; c = 2

now substitute these values in b² - 4ac = 0 that gives

[2(α - 12)]² - 4(α - 12)(2) = 0

=> 4(α² + 144 - 24α) - 4(2α - 24) = 0

=> α² + 144 - 24α - 2α + 24 = 0

=> α² + 168 - 26α = 0

=> α² - 12α - 14α + 168 = 0

=> α(α - 12) - 14(α - 12) = 0

=> (α - 14)(α - 12) = 0

=> α = 14 or 12