Use the discriminant to determine the number of real solutions of 3x2+6x−42=0 .(1 point)
The discriminant is given by the formula:
Δ = b² - 4ac
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, the quadratic equation is 3x² + 6x - 42 = 0.
a = 3
b = 6
c = -42
Plugging these values into the discriminant formula, we have:
Δ = (6)² - 4(3)(-42)
Δ = 36 + 504
Δ = 540
Since the discriminant (Δ) is positive (specifically, greater than 0), there are 2 distinct real solutions for this quadratic equation.