5. How many real-number solutions does the equation have? 9x2+12x+4=0
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
3 answers
A. one solution
explain
To determine how many real-number solutions the equation has, we can calculate the discriminant of the quadratic equation. The discriminant of a quadratic equation of the form ax^2 + bx + c = 0 is given by the formula b^2 - 4ac.
In the equation 9x^2 + 12x + 4 = 0, we have a = 9, b = 12, and c = 4.
Calculating the discriminant:
Discriminant = b^2 - 4ac
Discriminant = 12^2 - 4 * 9 * 4
Discriminant = 144 - 144
Discriminant = 0
Since the discriminant is equal to 0, this indicates that the quadratic equation has one real-number solution. This is because when the discriminant is equal to 0, the quadratic equation has one real solution (a single repeated root).
Therefore, the correct answer is A. one solution.
In the equation 9x^2 + 12x + 4 = 0, we have a = 9, b = 12, and c = 4.
Calculating the discriminant:
Discriminant = b^2 - 4ac
Discriminant = 12^2 - 4 * 9 * 4
Discriminant = 144 - 144
Discriminant = 0
Since the discriminant is equal to 0, this indicates that the quadratic equation has one real-number solution. This is because when the discriminant is equal to 0, the quadratic equation has one real solution (a single repeated root).
Therefore, the correct answer is A. one solution.