b2-12b+144=0
no real roots
use quadratic formula to get complex roots
The given equation is b^2 - 12b + 144 = 0. To solve this quadratic equation, we can use the quadratic formula:
b = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the coefficients of the quadratic equation are:
a = 1 (coefficient of b^2)
b = -12 (coefficient of b)
c = 144 (constant term)
Substituting these values into the quadratic formula, we have:
b = (-(-12) ± √((-12)^2 - 4(1)(144))) / (2(1))
= (12 ± √(144 - 576)) / 2
= (12 ± √(-432)) / 2
Since the term inside the square root (√) is negative, we know that the equation has no real solutions because we cannot find the square root of a negative number in real numbers.
Therefore, the equation b^2 - 12b + 144 = 0 does not have any real solutions.