Question

0=-3x^2+18x+27

A) one solution
B) two solutions
C) no solutions
D) infinitely many solutions

Answer 1

Since it only wants to know about the nature of the solutions, of
-3x^2+18x+27 = 0 or
x^2 - 6x - 9 = 0

b^2 - 4ac
= 36 - 4(1)(-9) > 0

so we have 2 real solutions.

Answer 2

If a and c have opposite signs, the discriminant is positive -- so 2 real roots

Answer 3

To solve the equation 0=-3x^2+18x+27, we can start by factoring out -3 from the equation to get:

0 = -3(x^2-6x-9)

Next, we can use the quadratic formula to find the roots of the expression inside the parentheses:

x = (6 ± √(6^2 - 4(-9)))/2
x = (6 ± √72)/2
x = 3 ± 3√2

Therefore, the equation has two solutions, answer choice (B).