To find the range of possible values for P in the equation 18^2 + 2px + 32, we can use the concept of discriminant from quadratic equations.
The discriminant (D) helps in determining the nature of the roots of a quadratic equation and is calculated using the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this equation, a = 18^2, b = 2p, and c = 32. Substituting these values into the discriminant formula, we get:
D = (2p)^2 - 4(18^2)(32)
D = 4p^2 - 4(18^2)(32)
D = 4p^2 - 4(324)(32)
D = 4p^2 - 41472
Now, for the equation to have any real roots, the discriminant D must be greater than or equal to zero. Therefore, we have:
4p^2 - 41472 >= 0
Simplifying the inequality:
4p^2 >= 41472
p^2 >= 10368
p >= sqrt(10368)
p >= +- 102
Hence, the value of P for which the equation 18^2 + 2px + 32 has real roots is P >= -102 and P <= 102.
Therefore, the statement "P > +/- 24" is incorrect. Please note that the expression "P > +/- 24" suggests that P should be greater than 24 or less than -24, but the correct range is P >= -102 and P <= 102.