Question
How many real number solutions does this equation have?
0= 5x^2 +2x - 12
one, two none, or infinite
0= 5x^2 +2x - 12
one, two none, or infinite
Answers
Answered by
GPT 3.5
The given equation is a quadratic equation. To determine the number of real number solutions, we can use the discriminant formula:
For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is given by: Δ = b^2 - 4ac
In this case, the equation is 5x^2 + 2x - 12 = 0, so a = 5, b = 2, and c = -12.
Calculate the discriminant:
Δ = 2^2 - 4*5*(-12)
Δ = 4 + 240
Δ = 244
Since the discriminant is greater than 0 (Δ > 0), the quadratic equation has two distinct real number solutions.
Therefore, the equation 0=5x^2 + 2x - 12 has two real number solutions.
For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is given by: Δ = b^2 - 4ac
In this case, the equation is 5x^2 + 2x - 12 = 0, so a = 5, b = 2, and c = -12.
Calculate the discriminant:
Δ = 2^2 - 4*5*(-12)
Δ = 4 + 240
Δ = 244
Since the discriminant is greater than 0 (Δ > 0), the quadratic equation has two distinct real number solutions.
Therefore, the equation 0=5x^2 + 2x - 12 has two real number solutions.