Use the discriminant to determine how many and what kind of solutions the quadratic equation 3x^2+4x=-5 has
To determine the number and type of solutions for the quadratic equation 3x^2 + 4x + 5 = 0, we will use the discriminant formula:
Discriminant (Δ) = b^2 - 4ac,
where a = 3, b = 4, and c = -5 in the quadratic equation ax^2 + bx + c = 0.
Substitute the values into the formula:
Δ = 4^2 - 4 * 3 * (-5),
Δ = 16 - (-60),
Δ = 16 + 60,
Δ = 76.
Since the discriminant (Δ) is positive (Δ > 0), the quadratic equation has two distinct real solutions.